There are buses that run from the resorts at that time of the morning. They start around 6.15. They are not as regular as they are just prior to, during and after park operating hours so you want to try not to miss one as there will be a fair wait for the next.
Opinions/approaches on this are divided and many prefer to use a taxi. We found we were just fine with the buses. We have done a 7.05 am ressie at CM and got there a good half hour early. We had allowed time to walk or take a monorail (not sure if the monorails run this early nowdays) from MK to the Contemporary but seeing as all the guests on the bus were headed for a breakfast, the bus driver drove us right to CR.