If you can drive, but prefer not to and are considering a couple of days serious shopping I would STRONGLY suggest you reconsider the option. Cost wise, getting taxis too and from the MAM from Disney is going to be at least $30 each way, to and from the Florida Mall is going to be close to $50 each way. Driving in the US is REALLY easy and from Disney both are easy to find.
For MAM, you'd take I4 East (sign posted to Orlando) and get off I-4 a couple of exits after Universal, you can see the Mall from I-4 on the right hand side of the road. Getting back take I-4 West ( signposted to Tampa) and take one of the Disney exits.
For FM I'd take Osceola Parkway out of Disney to Orange Blossom Trail then north on OBT until you see FM on your right. If you cross Sand Lake road you've gone too far as the Mall is on the intersection of OBT and Sandlake road.
Getting busses is going to be time consuming ( and a LOAD of hassle with bags), getting a cab is going to be expensive and potentially hassle waiting around for one to turn up. Renting a car for a couple of days is going to save you money on cab fares, and will give you much greater flexibility of movement. Unless there's a reason why you can't drive ( i.e. no licence) I think it's by far the easiest option, and maybe a couple of days would give you the confidence to try driving a little more on future trips.