When fingering the note "Bb" on the saxophone, we have a few different options:
SideThe first fingering I teach saxophonists is "side Bb", which is fingered just like the note "A" while simultaneously adding the first side key with the right hand (see below):
This is a great fingering, especially for fast chromatic passages where you might go from "Bb/A#" to "B" or "A" very quickly. It is also a good trill fingering when trilling up from "A". Many saxophonist who started on clarinet tend to favor "side Bb" as this fingering translates to the clarinet (similar to "Bb" in the upper register).
1+1Another much less used option is what I'll call the dreaded "1+1 Bb":
This is fingered by closing the first finger in each hand, aka 1+1. I do not favor this fingering on saxophone because it shuts a long row of pads in the middle of the stack, which can flatten the pitch and muffle the tone of "Bb". This means the color of your "Bb" might not match the adjacent notes. However, it is useful in a few situations. If you have a fast arpeggio or passage where you must go from "F" to "Bb", it can come in handy. However, even in these situations I'll most often use the "bis Bb" fingering.
Unfortunately, this "1+1 Bb" seems to be the fingering that band directors teach. This is very frustrating, as it's the least-used fingering among professionals. I can't imagine how much time has been wasted un-learning this fingering.
The "1+1 Bb" fingering can be modified to be "1+2" (using the second finger in the right hand instead of the first). This option might get you out of a jam in certain very specific situations where you'd be going from "Gb" to "Bb", or their enharmonic equivalents.
Bis"Bis Bb" (rhymes with "this") is executed by holding down the "B" key and the very small "bis" key at the same time with only your first finger.
Because you are only using your pointer, mentally this fingering is similar to "B natural". The difference is that your finger is positioned slightly to the south. This makes "bis" a very easy fingering to get to on the horn. I've also seen many jazz (and classical) players slide on and off of the "bis" key very quickly to execute grace notes or chromatic passages.
Among pros, I tend to see players using "bis Bb" the vast majority of the time.
See educator Greg Fishman's great YouTube video demonstrating his "Bis" technique: