Beet pulp is safe for rabbits. It's an ingredient in at least one rabbit pellet (Zupreem, I think?). I fed it to Gus for a few months when he couldn't have hay all the time. However, it is a much higher energy food than regular timothy hay, and bunnies will gain weight on it. At least Gus did. I eventually took him off it because he was getting tubby. But if I had nothing else to feed him, I'd have no reservations giving him the beet pulp.
Look for the high fibre brand (Fibre Max, I think?) if you decide to go that route. It's mixed with soybean hulls and has higher fibre and lower carbs.
Hope that helps!
Rue