Today I went to Starbucks with my bunny Sweetie. He kept still on my lap while I occupied myself. He doesn’t usually do that at home. There, he enjoys staying by me, but whenever I try to hug him he will run away quickly. We (who is "we"?) met a kind lady who kept five rabbits at home. As few people have pet rabbits, it pleased me to meet someone who shared that experience. Later, we went to a park nearby for fresh air. Sweetie jumped onto my lap even though I put him on the bench. I guess clinging to someone familiar makes him feel more secure in an unfamiliar environment.
Good work.
When you said "We met a kind lady...", I was a bit confused. Are you still at Starbucks or are you telling me a memory? Say something to tie the lady to Starbucks if that's where she is. For example, "A lady at the next table wanted to talk to Sweetie...".
We say "lap", not "legs". You could say "knees", but not "legs" unless you are lying down.
Were you inside the Starbucks? I'd be surprised if Starbucks allowed you to bring a rabbit inside.