Yes, but it's not free. Disneyland Express, operated by Gray Line. It's something like $35 per person RT. It's about an hour trip including stops at the DLR hotels. You do need to make a reservation. They also don't do the baggage delivery at all. You are responsible for your bags.
Natalie INTERCOT Staff: Disneyland Resort-California, The Water Cooler
We go to DL every August, mid month as my husband conferences at the DL hotel then. We have always used DL resort express, and it does stop at DL hotel first. However, the last time we went, we waited a long time for the next bus, and also, we missed the bus going back to the airport on our departure. We ended up taking a van back to the airport then, and realized how easy and inexpensive it was to cab it, and no waiting, and also leaving on our watch, not the buses. So...we are back again in April, and back again in August, and both times we will rent a car from the airport. We're done with the bus!!! We usually rent our car for sightseeing from Alamo at DTD, but this time we'll get it from the airport. Cost wise, it all evens out. When in August are you going? We will be there leaving on the 10th.
Multiple visits over Multiple years
30 plus stays at Disney's Polynesian resort