How I play Bb depends on notes before and after, some finger movements feel easier than others.
Targa has nailed it IMO. I would only add that some finger movements are more efficient and practical than others.
I have always taught that 1-2 + side is the "regular" fingering for Bb or if you will, the "default" fingering. It is the most practical fingering when Bb is preceded by A or Ab
and followed by C or Cb (B). This makes it the smoothest fingering in the F, Bb, Eb, Ab, Db, Gb, and Cb major scales. It is also the smoothest fingering in the chromatic scale.
The 1 - 4 fingering is the most practical when Bb goes to F or D or from F or D unless followed by C.
The 1 - 5 fingering is the most practical when A# goes to F# or from F# unless followed by C.
The Bis is the most practical when Bb follows a G or A unless the Bb itself is followed C or B natural.
The "unless followed by C" business is all about avoiding what I call the "flip-flop" ---exchanging the first and second fingers. This is also true on the right hand playing F to F#. The fork fingering for F# is used to prevent the "flip-flop" on that hand.
I know that this sounds very "pedantic". That's because it is. I have taught this stuff for years and have found that choosing the best fingering is really nothing more than just using "common sense". In slower music just about any fingering---regular or alternate will work. It is at the faster tempos and shorter note values, that the smoothest finger combination can make all the difference.
An easy way to test one fingering against another is to play that note as part of a trill. First with the note that precedes it, and then with the note that follows. If anyone likes sliding the first finger on an off the bis key, try doing a Bb - B trill using that method and you will see what I mean.