reflector and honeycomb grid
I'm not intimately familiar with that exact strobe, but I recently bought a shorter modeling bulb for my Alien Bee strobe because of a similar problem with a beauty dish. The one I got was 150W, but here's the 250W version at BHPhoto:
That's 3.58 inches long with a regular male bulb connection (not sure if Bowens uses the same type, but maybe). Actually looking at the first review, the fellow apparently used it on a Bowens 500R strobe. Check your bulb's length, and I bet it's a good half inch+ longer than this one.