Because it's cheap and easily available, I make almost all of my bows out of hickory backed red oak boards. If you're making just a plain flat bow, an 1/8" hickory strip doesn't really add any draw weight to the bow, but it prevents any "less than perfect" oak boards from lifting splinters.
I once took a piece of 1/8" thick x 2" wide x 6' long hickory that I had cut as a backing strip that had countless bad spots in it and tried to break it... I was able to tie the blessed thing into a knot before I heard the first crack. Even then, it didn't lift a splinter, just snapped. This stuff is amazing!
As for an R/D bow, the hickory backing will make the bow hold its shape during glue up. I've not make one like this before, but I've used the hickory to glue in some pre-stress, and its works like a charm. I'm sure "pre-stress" isn't the right term - that's what we call it in the construction industry when a beam is pre-bent in the opposite direction of a load.
Something I've learned recently - make sure your wood is dry! Buy a moisture meter, and be sure your wood is around 6 to 8% moisture content before you start tillering to avoid massive set. I recently have been doing this, and I've brought 3 inches of set down to 3/4 of an inch of set. SCORE!!!!