When BD is exhausted he cant use other rhythmic abilities. So if you use Sprint, you have to wait 30 seconds to use Sidestep and other rhythmic abilities. Through there is a talent that lowers it to 20seconds.
My guess would be you wouldn't be allowed to use another Rythmic Action until the exhaustion ends.
There are talents reducing the exhaustion by 10 secs, and increasing the Rythmic Action by 3 secs...there's still at least a 2 sec gap with most of the Rythmic Actions (some have a 60 sec exhaustion, so I doubt it would be time without energy).