If your engine bay is 1/4 full of water after riding a bit, either you have a serious leak somewhere, your hood hood isn't on when you rollover or flip, or your bills are plugged. I rode my BoB with one of my 2 cooling lines running to my manifold off for about 6 months. I changed my starter once and BAM. Found a loose hose. Only reason I know it was for that long was because if I had my bilge on while riding, it would always trickle a little bit of water. I thought I had a leak somewhere in the midshaft or something. Just rode it out.
A bilge is not required to keep water out of your hull. Put a go pro in your hull with a light source and figure out where your water is coming from if you need to.