AFAIK, there is no Disney (free) transportation to Mass - and there is no longer any Sunday Mass celebrated on site. If you will not have a car, believe your options are a taxi or the Mears shuttle. Here are some recent threads on the subject:
It was reported on these boards that the masses were discontinued b/c the local churches were having difficulty supplying the priests. I may be wrong, but I believe it was the churches rather than Disney that discontinued them.
For a long time there was a letter on the Mary Queen of the Universe Shrine site (I think that is what it is called) explaining why they no longer went to Disney. Basically it was related to the priest shortage and the fact that they now had this great facility for you to go to.
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