As a fun fact, both Cyrillic letters Б б sounding "b" and В в sounding "v" were historically derived from Greek Β β.

B/V shifts or mergers are very common, notably in many Spanish variants they will, for example, write “vaca”, betraying the latin root “vacca”, but very clearly say “baca”. Coming from a language that clearly differentates between these sounds, it’s surprising how close they are.

For ancient Greek, two great books are:

Greek: an Intensive Course by Hansen and Quinn.

Basics of Biblical Greek by William Mounce

Both are standard texts with solutions easily available online.