You could probably do it if you made the bamboo very thin
Tim Baker argues that rather than thinning (which I WOULD do) narrowing is even more important, so trapezoidal limbs are in order. Almost all the tension/compression forces are felt in the first 10% of limb thickness, both back and front, the back barely stretches at all, and the belly must take the load. Dauntless's bow that Darksoul posted a link to is a perfect example of how to pull it off. Notice it is wide where it bends, trapped, and reasonably long.
NOW, that said, BACKED bows fail in compression for the same reasons SELF bows do. Elm is great in tension, and mediocre in compression, and there are a LOT of wonderful elm bows out there. Now, boo is even better than elm in tension, and oak is (in my experience) worse than elm in compression, BUT if the boo was thin and trapped, and the oak was wide and dense, you could make it work. Red oak varies a LOT in density. I had a flat sawn craft board once where the entire 1/2" thickness was ONE growth ring and a little bit on the edges. SG was like 0.74; very heavy for oak.
Another consideration (not to get too fancy) is the use of the Perry reflex to relieve some of the belly compression strain on the oak. If you went R/D by using steam to deflex the handle area, then pulled it back to reflex, that mioght help. Gotta warn you, though tillering a R/D bow is weird.
So, there's about all i know about it. And all that said, I still think you'll be ebtter off backing stiffer wood with bamboo; at least as hard as black locust, say. Or much more elastic wood, like yew or juniper.
