how would a
bowrider handle those sort of conditions?

It's hard to give a definitive answer, since there are a lot of variables
such as the wave height, the wave period, and the exact style, weight, and
loading of a given bowrider.
If you take a bowrider out into a sea that is too large for the boat you run
the risk of having waves come over the bow and into the boat. If this
happens repeatedly it will overrun the capability of the bilge pump and
start filling the boat up, causing a loss of manouverability or worse.
Having the boat full of people will increase the pitching of the boat and
cause the boat to dive between waves more, and if the waves are close
together you can stuff the bow into the next wave. The way you handle the
throttle and trim can also make a big difference in the way the boat can
handle the seas.
If you could find a bowrider that has scuppers with a closed bilge that
would be good for you if you intend to operate in rough water a lot, or
maybe you need a boat with a closed bow.