I had the same decision to make getting to Tampa for a cruise even though I live 25 minutes from Port Canaveral. Uber, private shuttle, friends, forcing children to drive 5 total hours round trip for us, etc. were all rejected options... At the end of the day, the easiest choice was to rent a car and drive it to Tampa, drop off people and bags at the terminal and then walk 10 minutes from the car drop-off area to the Cruise terminal. Easy stuff and would highly recommend it unless you can't cover less than a mile on foot.
Cost me roughly $70 including tolls and gas. Of course, depending on your party size and bags, you may need to scale up the size of your vehicle and it may cost more.
Finding gas on the way to the port was easy. Ask your phone to plot your course!
