[villagetinker]

This is an interesting idea, and probably the only entity that could pull this off would be villages transportation. I am guessing that it would not be a profitable business, but I could be wrong.
Consider the following:

There were problems in the past with tour buses using the squares, and having cars parked for extended periods, so the bus pickup and drop off locations would need to be some distance from the squares to avoid the previous concerns, IMHO.

It would probably take an hour for a single bus to make a loop to all 3 squares, this may be too long for people to wait, especially if it is raining.

If you just missed the bus, then you have up to an hour wait for the next one.

During a very popular event (parade, show at the Sharon, farmers market, etc.) I could easily see more people arriving then seats available on the bus, while at other times the bus would be mostly empty.

It would be an interesting comment for the annual survey, and POA or VHA meetings to see if it gets any traction.

On a personal note, we go from the Brownwood area to the Spanish Springs square area 3 times per week, and would not use a shuttle or bus if it was available. We can make the trip by car in 20 to 25 minutes, and parking is typically available, except during the days with parades. The shuttle/bus would simply not be as convenient as our own car. This may change in the future, if we are no longer able to drive this distance, or at night.