First, I sometimes act more monkey than I really am just because I can't or won't allow the bunny to be vulnerable.
Would you be able to allow the bunny out more if you were with someone 1) you were in love with WHO 2) was in love with you in the way you wished your 2bx had been, AND 3) the guy was the kind of guy that you knew when you were going to see him again or at least knew he would call when he said he would call?
It seems to me that your bunny's tendency to stay in the hutch is a very wisely self-protective instinct on her part. She's very smart, which is why she deserves belly-dancing lessons AND a trip to the art store. (Stop doing the 7 thing and PLANNING what you're going to do and just do SOMETHING for her! Go get the drawing supplies-- she's wanted them for years.)
I know... everything precipitates a Lil story: years ago I met this guy kind of casually who was so nice and attentive, funny, friendly, considerate, etc. I liked him from afar. One day we found ourselves seated next to each other at a professional luncheon. We started chatting, laughing, telling stories-- we liked all the same books, movies, yaddayaddayadda. There's an annual festival in my town that has hundreds of events, and soon after this luncheon, he called me and asked me to attend one of them with him. He was teaching at a university in a nearby town and he said, "When I get out of class on Tuesday (or whatever), I'll call you." When he said that, I had NO DOUBT in my mind that he would call me when he said he would-- it was a gut feeling (and a very refreshing one at that!). He did, we went, we became very close friends..... but.... of course, he turned out to be gay. When my H and I got married, we had our reception at his home. (He and his partner are both gone now-- aids.) (And Lil's story always ends with someone being dead....)