To your last point, LE suspects he rode the bike down to the hotel that morning since it only took him about 10 minutes (
source).
I took a walk around the crime scene area yesterday. The gap between 54th and 55th streets is massive and full of cameras. If the bike was placed there, I’m surprised that this information hasn’t been released. It seems like LE doesn't know when he got on the bike to flee northbound, or perhaps they’re just not stating that publicly.
Maybe the bike was locked up on 55th street. I read that he had the bike battery with him, and I‘lol venture that the bike was locked up. It’s not a 100% guarantee that the bike and/or battery would get stolen while he was committing the murder if it wasn’t locked up, but it doesn’t seem like a risk this particular suspect would take.