My reccomendation is to call your hotel and find out very specifically how the shuttle operates. Some hotels have hotel to park service on a regular schedule; others have a morning run to the Ticket and Transportation Center, and then an evening run back to the TTC to pick everybody up.It varies from hotel to hotel.
It sounds like your sister may have been staying on Disney property, because the only busses that drop you off at the gate, are the Disney busses.
I can't give you specifics on how long it takes from maingate to park entrance because it varies from park to park, and day to day depending on traffic flow and whatnot. Your longest commute will be to the Magic Kingdom. You have to park at the Ticket and Transportation Center, and take the monorail to the Magic Kingdom.
I've NEVER had to wait long for a tram, either. The trams run fairly regularly, and there's always been one waiting for us right after we parked.