I get on the bike by slightly angling the frame towards me and swinging my good hip over it. My surgeon and PT encouraged me to do lots of range of motions exercises which helped a great deal. When I am done riding if i am very tired and I don't have a stable support (garage/car etc.) that i can rest on, I while lay it down to get off. I am more cautious when i am tired.
My biggest limitation is not the hip or my overall fitness, its the knee on my opposite leg that I had replaced last summer. I've had to raise my seat more to accommodate the lack of knee range of motion which has made me even more cautious getting on/off the bike.
Take it slow and listen to your body-it's worked so far for me.