The existence of a distinction for some speakers between a verb pronounced /ˈbaɪfɚkeɪt/ (with primary stress on the first syllable) and an adjective pronounced /baɪˈfɝkət/ (with primary stress on the second syllable) appears to exist because for over two centuries, there have been two patterns for stressing polysyllabic words ending in -ate, and one of these patterns ended up becoming more common for verbs than for other parts of speech.
The Oxford English Dictionary entry for contemplate summarizes the situation as follows:
In a few rare cases (Shakespeare, Hudibras) stressed ˈcontemplate in 16–17th cent.; also by Kenrick 1773, Webster 1828, among writers on pronunciation. Byron, Shelley, and Tennyson have both modes, but the orthoepists generally have conˈtemplate down to third quarter of 19th cent.; since that time ˈcontemplate has more and more prevailed, and conˈtemplate begins to have a flavour of age. This is the common tendency with all verbs in -ate. Of these, the antepenult stress is historical in all words in which the penult represents a short Latin syllable, as acˈcelerate, ˈanimate, ˈfascinate, ˈmachinate, ˈmilitate, or one prosodically short or long, as in ˈcelebrate, ˈconsecrate, ˈemigrate; regularly also when the penult has a vowel long in Latin, as ˈalienate, ˈaspirate, conˈcatenate, ˈdenudate, eˈlaborate, ˈindurate, ˈpersonate, ˈruinate (Latin aliēno, aspīro, etc.). But where the penult has two or three consonants giving positional length, the stress has historically been on the penult, and its shift to the antepenult is recent or still in progress, as in acervate, adumbrate, alternate, compensate, concentrate, condensate, confiscate, conquassate, constellate, demonstrate, decussate, desiccate, enervate, exacerbate, exculpate, illustrate, inculcate, objurgate, etc., all familiar with penult stress to middle-aged men. The influence of the noun of action in -ation is a factor in the change; thus the analogy of ˌconseˈcration, ˈconsecrate, etc., suggests ˌdemonˈstration, ˈdemonstrate. But there being no remonstration in use, reˈmonstrate, supported by reˈmonstrance, keeps the earlier stress.
So it used to be possible to pronounce not only polysyllabic adjectives ending in -ate, but also polysyllabic verbs ending in -ate with stress on the penult syllable, if the penult syllable was "closed" by a coda consonant in Latin.
However, stressing heavy penult syllables in polysyllabic -ate words became less common over the years, especially for verbs. I would guess that antepenult stress in words with heavy penult syllables has come to be more strongly established in verbs because, as others have pointed out, in verbs the ending -ate is pronounced with an unreduced vowel /eɪ/, which can be interpreted as a type of stress (according to some theories of stress), and English speakers have a tendency to prefer to stress alternating rather than adjacent syllables.
Another similar example that I know of is the verb consummate vs. the adjective consummate; the OED entry for the verb says
N.E.D. (1893) records also the pronunciation (kǫ̆nsɒ·meit) /kənˈsʌmeɪt/, with stress on the penultimate syllable. This pronunciation is listed in dictionaries until the late 19th cent.; sporadic evidence of the shift of stress from the penultimate to the antepenultimate (i.e. the first) syllable is found from the late 18th cent. onwards, but dictionaries and especially usage guides were slow to recognize it. From the 20th cent. onwards dictionaries record only first-syllable stress.
[...] In the adjective consummate adj., both penultimate and antepenultimate stress are still found. N.E.D. (1893) recorded both stress positions in the adjective, noting that penultimate stress was ‘still usual’ at the time, but antepenultimate stress was also frequent.
As a matter of fact, some sources indicate that it is possible to stress the second syllable of bifurcate even as a verb: Merriam-Webster says "verb bi·fur·cate \ ˈbī-(ˌ)fər-ˌkāt , bī-ˈfər- \" and the American Heritage Dictionary says " (bī´fər-kāt´, bī-fûr´-)".