Hmm, I don't know what to say. Unless you're in a very specific situation which requires something like this, this sounds like too much and like it's encouraging transference and boundary crossing in a non-therapeutic way. There are plenty of ways most issues could be dealt with that don't involve going to a ballroom dance with your therapist, so I find this to be a questionable offer. Plus you say it might feel odd to you as well. I wonder if you feel like your own boundaries are being crossed by this invitation. I want to mention, I'm really not one against out of session contact or flexible boundaries and atypical approaches in therapy. It's just that this sounds unnecessarily personal to me. Maybe it's just me. Then, you posted the update, so I thought I'd post my thoughts, in case something might prove useful to you.