A bamboo backed bow can in general be shorter than a selfbow. Bamboo can bend really far before it breaks. However, the belly must also be able to resist the sharp bend. A bamboo backed balsa bow could not be made any shorter than a balsa selfbow, because the balsa would be the limiting factor. The balsa would fail in compression long before the bamboo would in tension.
The minimal safe length of a bamboo backed ipé (BBI) depends on many factors, such as draw weight, draw length, limb width, stiff handle yes or no etc. The shortest BBI I've seen and shot was (I think) 58" NTN, stiff handle, R/D design, about 1˝" wide, 65#@28". In my opinion, this bow was underbuild. But it held up, and goes to show how much a BBI can take. Lowering the draw weight to 50 pounds would have made that particular bow much safer. I'm sure a bend-through-handle bow could be made even shorter, and 56" for a 28" draw length should not be a problem if designed properly.