Still not eating :/

[Bogertophis]

Is the cork tube open at both ends? If so, & despite the fact that she appears to like it, you might want to cover (enclose) one end with something for added privacy.

It should be obvious that a cat has no business being anywhere near a snake cage...and your snake can smell your cat, even if you cannot. Cats are predators...BPs are
prey! Keep the cat out of that room from now on.

Rather than throwing a towel over the front, I'd suggest covering the back & sides with some scenery (unless you like the look of insulation) & then insulating behind
that (corrugated cardboard, foam board, sheet cork, styr-foam, peel & stick carpet tiles...many things work fine to both insulate the tank and add privacy). I would also
consider installing something along the front, just maybe 4-6" worth for added privacy.

It sounds to me like your snake realized she was being watched when she recently grabbed the rat & then left it out of an abundance of caution. You need to become a
"ninja" when she takes food next time...FREEZE! then move away so slowly that she cannot POSSIBLY notice. Many snakes besides BPs are distracted & intimidated
when there's any motion nearby & they're trying to eat...in the wild, that motion could be a predator coming for them when they're vulnerable (mouth full or slow moving
with a meal), & your snake does NOT know you by visual appearance...thus, you standing there is perceived as a threat.

Feed in evenings, low light, wear dark clothing & learn to be still. A towel over the front of the cage will only be a bigger shock when you remove it...change = threat.
You still aren't thinking like a Or keep another kind of snake that's less-easily intimidated.

For example, I have corn & rat snakes that either ignore my motion, or drop the prey to chase me thru the glass instead. More fun to feed, just saying...