Welcome to the one drawback (in my mind) of the inmast furling. I have no solution. In the winter, I insert a bung in the most forward bilge section limber hole. This prevents water from filling the entire bilge, and if ice forms, from damaging the bilge pump, float switch and my AC intake strainer.  I dump some -50 degree antifreeze in the forward section to minimize ice formation. Then, after every winter rainstorm, I pump the water out with a small hand operated bilge pump and poor in more antifreeze. With deep freeze forecasts, I add salt to the antifreeze to minimize ice build up. It's a pain.
 I'm going to tape the mast/mast collar inside the mast boot to improve the mast/deck seal. I notced some water trickles past the spartite down the exterior of the mast into the bilge. Maybe this will help some

Also, after removing the mainsail for the winter, I haul up and wrap a 1" line around the furing shaft. This dampens the the loud clanking from the furler hitting the inside of the mast during high winds.

Maureen,
That seems to be a fairly normal issue with the in-mast furling.  One on our members posted a they fixed it by sealing the openings on the mast head (https://www.catalina36.org/forum/general-discussion/dry-bilge-last).  It’s on my to do list to try this.
 

It is a chronic problem as far as I can see. During the rainy season, I keep a small cheap wet/dry vac aboard and use it to keep the bilge dry. I just empty it down the sink.