We've done this before, never used Uber, used Mears shuttle (wasn't overly impressed) to go from Disney to Uni and back. It was fun but a little rushed of a day. We fit probably 75% of what we wanted to see in.
With only one day and no express pass, make sure to have some kind of plan. Make a list of what you absolutely have to do verses if we have time to do. This way if you run out of time, you'll still hit your top choices. Keep an open mind and try not compare everything to Disney. Just enjoy Universal for what it is, and you will have fun. I'd skip a long lunch to help maximize park time. Then, I'd either do a later dinner in Citywalk before returning to Disney or make a late ADR somewhere on Disney property maybe at DS or at one of the hotels.