You can reach Biysk by train from Moscow, Novosibirsk, Krasnoyarsk and some other cities. Check itinerary and prices at the official website of Russian Railways. Address of train station: Biysk, Shukshina street, 4
There are everyday public buses from Novosibirsk (6 hrs), Barnaul (3 hrs), Kemerovo (10 hrs), Tomsk (11 hrs), Novokuznetsk (5 hrs). Address of bus terminal: Biysk, Vali Maksimovoy str, 86. Phone +7 (3854) 405248. Official website.
From Novosibirsk to Biysk you can travel by private car along Chuysky tract (highway P-256), following to the south on the route Novosibirsk-Novoaltaisk-Biysk (distance 359 km, 5 hrs on the way).
The closest airport is Barnaul (BAX), 160 km to the north from Biysk. How to get to Barnaul. Then by train or public bus.