I'd just put on a long sleeved something (jersey or running tee long enough to cover your back) and wear it for the bike and run. If you're concerned about getting too warm between the bike and run, arm warmers might work, but they might also be hard to put on. I'd probably wear one of those long sleeved running tech tees or wool that breathe well in case I got overheated (and considering my body will still be wet...)

I would pack with you the short sleeved and long sleeved options just in case.