Hi, Marcy!
Staying at Disney's Polynesian Resort? Wow, are you in for a treat!
Disney's Hollywood Studios does not currently have a bus to Downtown DIsney.
However, you can take a bus to Saratoga Springs Resort and Spa, which is the closest resort to DD, then either walk or switch buses at the resort. When you board the SS bus, ask the driver for the name of the stop that is closest to DD (it's usually the last stop of the route). The driver will also be happy to remind you when to get off the bus, if you're unsure. From that stop, you can walk to DD in under 10 minutes. If you don't want to walk, you can simply get off at the first stop at SS and wait for the next bus to DD. From DD, you can simply take a bus back to the Polynesian.
From the Polynesian, I wouldn't go to the Transportation and Ticket Center unless you need to transfer monorails to get to Epcot. In the time it will take you to get to TTC, you might have gotten onto a bus to HS or AK. Just hop on the bus at your resort. Check out
this link to Transportation Information from Disney's Polynesian Resort for more details.
Also according to this list, you would need to transfer at Downtown Disney to get to another resort, so I don't believe that you'll share your Polynesian bus with another resort (It would be listed there, so that guests with dining reservations might be able to discover the quickest way from one resort to another.)
Hope this helps! Please ask any additional questions you may about your upcoming stay! We love to help!