A bassoon is a large woodwind instrument with a low range and a double reed. In music the larger the instrument, the lower the notes it plays.
Bass and baritone may be used together or separately to describe singers with low and lower voices. A family of instruments may include a bass one, but things are not always what they seem. The range of a bass recorder is equivalent to an alto singing voice, but the music for it is written in the bass clef and sounds an octave higher than written. A double bass is a large string instrument in an orchestra. It plays music which sounds an octave lower than the written notes. A similar smaller instrument in a jazz ensemble (for example) would be called an acoustic bass (even when amplified) to distinguish it from a bass guitar, which comes in electric or acoustic forms.
What else begins with B?
A brass band includes various instruments. If you want to know about a barrel-organ, please come back later, I am mentioning that in a week from now.
A banjo is a stringed instrument unlikely to be found in an orchestra. Bagpipes are often associated with Scotland, but there are other similar instruments from other places. Bagpipers may practise (without using the full volume possible with the bag) by using a chanter on its own. But that begins with C…