The earliest mention in Jaina texts of Bengal describes this as a primitive place with bad food, culture, and language; where mahAvIra jaina was attacked by pet dogs. But the religion did enter Bengal relatively early: and some of the early Jains (e.g. jainasUri bhadrabAhu) are mentioned to be from Bengal. If the evidence of the jaina texts are taken at face value, then around the time of ashoka (3rd-4th cent BC), jainas are already present in sizeable numbers in north bengal. In fact, the tAmalittiYA, koDivarSiYA, poNDavardhanIYA, khabbaDiYA sects are named after places in Bengal. Tradition also has it that bhadravAhu led some jainas to karNATaka to avoid a long famine in bengal, and these people formed the later digambaras; whereas the ones who stayed behind formed the svetAmbara sect. In 2nd century AD, a jaina from rArA built a statue of jaina in mathurA.
This religion also had a sizeable hold in Bengal, though they merged into Jainism later (their founder, makhaliputra gosAla was a friend of mahAvIra jaina). See here for some information about their views.
The buddhists, like the jainas and AjIvikas, were in Bengal very early, and buddha is said to have come here. Archaelogical evidence clearly shows buddhist presence by the time of ashoka, and its prominence by the second century B.C.: a dharmadattA and a RSinandana of pUJavaDhaNa contributed to sÃcI. However, in first century B.C., dutThagAmaNi of siMhala did not invite any theravAdIs from bengal, though chavaggIYa theravAdis are mentioned in Bengal. Tibetan sources however talk about nAgArjuna establishing a number of vihAra in Bengal. It is in this second century AD, that the buddhists split into the traditional hInayAna and mahAyAna.
In the early historical period, the vedic-puranic religion was probably not very strong in Bengal: in fact, this ‘aryanization’ of bengal probably did not happen till the post-Gupta period. A number of features of Hinduism, however, can be traced to non-indo-europen origins. In fact, it was during this early period that the writings of manu (1st century BC) and the development of the six schools of philosophy which started to define a hinduism clearly recognizable today; but none of this may have influenced contemporary bengal.
The tribal religions in Bengal today has a large emphasis on the worship of non-animate spirits embodying the world around us: the places, rocks, trees and forests playing an important role in these beliefs. There is little reason to doubt the ancient origins of this complex; and, indeed, a large part of folk hinduism seems to consist of similar beliefs. Thus, for example, the veneration of the tulsi plant, the vaTa tree, or the seora tree; the planting of a branch in the sacred areas as a symbol of the tree; the use of parts of the banana plant as a symbol of a married woman; the use of an ear of paddy as a part of the ceremony; the grains of rice and stalks of durvA grass used in benediction; the use of turmeric in washing the bride during marriage; the use of Ak, cAl-kumD.A, banana, betelnut, pAn, turmeric, coconut, vermillion, cowdung, kaD.i, khai, yoghurt, etc. in various ceremonies; and the traditional associations of certain animals with certain gods probably point to a significant Indian, and bengali, contribution to the common hinduism. In fact, it is likely that many of the current Hindu divinities like shiva, kAli, karAlI, nArAYaNa shilA, gaNesha, bhairava, and Buddhist ones like jambhila, hArItI, ekajaTA, nairAtmA, bhRkuTi etc. are of non-aryan origin. The seals from the Indus Valley Civilization clearly show animal and plant figures, as well as a human figure that recalls the Hindu meditating shiva's association with animals. The expatriate Meluhha communities (possibly, from the coasts of gujarat) in Sumer and elsewhere seem potray the cow in preference to the dominant unicorn motif in the homeland, and may have had names referring to a cow goddess.
However, the nature of this early religion is difficult to ascertain today. In the modern world, we do find sacred places, sometimes even without the idol of any god, which are held sacred, and to the god of which local people promise and sacrifice so that their hopes be fulfilled. These village deities have various names in various places, and have often been identified with the higher pantheon of hindu gods and goddesses. Their worship has not always been sanctioned by hinduism—manu very often calls their worshippers fallen hindus—but they still remain a very important part of folk hinduism. In fact, some of the hindu deities like shitalA, manasA, vanadurgA, SaSThI, caNDI, kalI, shiva, parNashavarI, jaGgulI are almost definitely of non-indo-european origin. The dhvajApujas definitely formed a part of ancient bengali folk tradition; at least, descriptions of indradhvajA survives from before the 11th century. Similarly, one finds descriptions of sacredness of the vaTa tree and its association kith kubera and lakSmI, descriptions of animal sacrifice and worship of stones and places, and descriptions of the gods of agricultural products and processes like extraction of sugarcane juice. The various processions like rathayAtrA, snAnayAtrA, dolayAtrA involving music and dancing can also be traced to the ancient period: in fact emperor Ashoka has edicts against such activities; but mention of agastyarghyayAtrA (during dashaharA), aSTamI snAnayAtrA, mAghIsaptamI snAnayAtrA in kAlaviveka etc. point to their persistence in a much later part of the ancient period.
The other important ingredient of Bengali lifestyle: the frequent observance of vrata, especially by the womenfolk, is also a very old tradition. Most of these are dedicated to gods that were non-aryan in the beginning; and a lot of miracles and fertility symbols pervade them; and early writings speak against them. However, the puranas seem to accept some of these (e.g. shivarAtri, akhaNDa dvAdashI, pURNimA, nakSatra, dIpadAna, Rtu, kaumudI, anaGga traYodashI, rambhAtRtIYA, mahAnavamI, budhASTamI, ekAdashI, naksatrapuruSa, AdityashaYana, saubhAgyashaYana, rasakalyANI, aGgAraka, sharkarA, ashUnyashaYana, anaGgadAna) within the Hindu fold, but we do not know which of these were practiced in ancient Bengal. Some of the ancient vratas mentioned in kAlaviveka include sukhrAtri (kArttika), pASANa caturddashI (agrahAYaNa), dUta pratipada (kArttika), kojAgara pURNimA (Ashvina, though not related to lakSmI), bhrAtRdvitIYA (kArttika), AkAsha pradIpa (kArttika), akSaYa tRtIYA, ashokASTamI.
The worship of dharmaThAkura and nIla or caD.aka seem tribal traditions, in form (and even today require participation by the untouchable castes in some places). There is some indication from shUnyapurANa (written in medieval times) that these traditions were already present in ancient Bengal. It is not known how old the tradition of ambubAci is.
Holi or holaka (in phAlguna) is clearly mentioned in dAYabhAga. It seems that it arose out of pastoral festivals merging with jhUlana (in caitra) mentioned in the 2th-3rd century (in rAmagaDh.a) and kAmamahotsava (in caitra) which one can trace back in various parts of north India to at least the fourth century, and whose trace is visible to at least the sixteenth century. In some parts of India, the fire for this festival has to come from the house of a shUdra.
We also finds idols of manasA whose worship (though not in idol form) is still common in bengal; and indications are that she was worshipped even in the early pala period. It has been conjectured that the origin might be from the dravidian mancAmmA and ambAvaru. The Buddhist jAGgulI is probably a related concept. The Buddhist parNashavarI was also worshipped in ancient Bengal. Similarly, during durgotsava, shavarotsava was popular. lakSmI was also worshipped, as were SaSThI and hAritI.