I agree with Flix. You can come up with cunning ideas to pack (or hide) a bow, but you still need arrows and it isn't simple to have take-down arrows.
I've wrestled with this one quite a bit.
You could use a crossbow with short bolts.
I can draw a 27 or 28 inch arrow, but I changed my shooting style to use a 23 inch draw. It is generally easier to find shorter natural shoots in this size for arrow making, plus there are other advantages. (But a longer draw should give your arrow more power, so it is a trade-off). But even a two-foot long arrow isn't easy to keep out of sight or stow in a pack.
Nowadays I don't use my bow and arrows much at all. I have found simple snares to be much more productive, although you need to be spending a fairly long time in an area (overnight for instance) to give the snares time to catch something.
Maybe some cord for snares and a decent rubber slingshot might be more practical for meat procurement. If a gun is out of the question and a weapon is desired, then maybe a hiking staff with a detachable Cold Steel Bushman spear blade would suffice.
But if you solve the stowable bow and arrow problem, I am keen to learn about it.
Best wishes... Coote.