From first preview until June 13, 2017, Bette is scheduled to perform all eight performances per week. On Tuesday evenings starting the 13th, Donna Murphy will be playing Dolly. Bette is scheduled to do the other seven performances per week.
Cowboysfan84 said: "2) How long is Bette Midler signed on to be with the show? One year?"
It did seem telling (to me anyway) that when Bette's tickets went on sale, they went all the way out until January 14, 2018. So, I have to imagine that is her last contracted day (at present)? I'm just speculating, of course, but it is rare to sell tickets so far out the day they go on sale.
And plus they're still not selling tickets for Tuesdays between June 13 and January 14, or for the entire first week of November (presumably Bette's vacation), so it's safe to assume that the reason they're selling tickets for all other days is because Bette is contracted to appear on them.