Hello, Maria!
Generally speaking, according to
Walt Disney World's Complimentary Resort Transportation page, transportation, including buses, is available one hour prior to Disney Theme park opening and up to one hour after Disney Theme Park closing. Keep in mind that Extra Magic Hours are offered at select parks at either morning or evening, so resort transportation will be calculated according to those additional hours.
That link also includes ways to get from one park to another. While a stop at the Transportation and Ticket Center may be required, there are sometimes quicker methods to do so as well. When you get to your resort, pick up a copy of the very handy, and complimentary, "Your Guide to the Magic!" In the most recent copy I received, there is a very handy chart on page 27 which informs Guests of how to get to parks, Downtown Disney, ESPN Wide World of Sports, miniature golf and more. There, it states that (at the time of publication) there is a bus which runs from Disney's Animal Kingdom Theme Park to Disney's Hollywood Studios. There is also a bus which runs from Epcot to Disney's Animal Kingdom Theme Park as well a bus which runs from Epcot to Disney's Hollywood Studios.
Transportation to Magic Kingdom from another park includes one extra stop, one for a bus and one for either a ferry or monorail from Transportation and Ticket Center. Once you get the hang of it, though, it's really very easy. We actually schedule a meal at Chef Mickey's when we decide to spend the rest of a park-hopping day at Magic Kingdom. This allows us to take a bus to Disney's Contemporary Resort from any other park. After our meal, we simply take the monorail (or even walk) to Magic Kingdom, thus eliminating a stop at TTC (plus, a meal with Chef Mickey is usually on our To-Do list!)
Send more questions as you think of them; I'd love to help you plan!