WIthout using the IPA symbol, I think "eh" would be the closest sound to the "i" in bit.
I an guessing on the accents, which I have bolded. In general, It seems like the second to the last syllable in a word is accented. Please correct me if I have made any errors.
Word - - - - pronunciation (translation into English)
пианисты, pi-a-nis-teh (pianists)
спортсмены, sports-me-neh (sportsmen
директора, di-rek-to-ra (directors)
пилоты, pi-lo-teh (pilots)
президенты, prye-zi-dyen-teh (presidents)
студенты, stu-den-teh (students)
секретари, syec-rye-ta-ri (secretaries)
банкиры, ban-ki-reh (bankers)
менеджеры, mye-ne-dzhye-reh (managers)
офицеры, ofi-tsye-reh (officers)
профессора, pro-fyes-so-ra (professors)
министры, mi-ni-st-reh (ministers)
бандиты, ban-di-teh (bandits)
ковбои, cov-boi (cowboys)
актёры, ac-tyo-reh (actors)
доктора, doc-to-ra (doctors)
инженеры, in-zhe-ne-reh (engineers)
журналисты, zhur-na-lis-teh (journalists)
боксёры, boc-syo-reh (boxers)
программисты, pro-gram-mis-teh (computer programmers)
таксисты (tac-sis-teh) Taxi cab drivers