Most hotels have shuttles to Disney. However, you will do so much better and get around far faster if you rent a car. Those shuttles run on a schedule, and some of the drop offs/pickups are hours apart.

Which hotel are you staying at? If you call them you might be able to find out what the schedule is.

If you stay at a Disney owned hotel you will be able to use Disney's Magical Express and then their internal transportation. However, the price differential is probably not worth it.

Cab fare to/from MCO is not all that cheap for 2 people or even a family. The price differential is not all that much, in my experience.