Another way to do it and still use Budget is to call for a taxi as soon as you get off the ship. Have some taxi numbers already in your phone from the Port area.
This was my plan last month because the Budget shuttle line was very, very long....we wound up waiting 25 minutes for a taxi to come (still shorter than waiting for the shuttle). The CM in the parking lot said taxi automatically come, but they are few and far between unless you specifically call for one. I just wish I had programed taxi numbers into my phone first, instead of just waiting for one to show up.
One other time there was a taxi waiting right there and we took it to Budget for $7.00.
MJ