Do you have a shuttle from Ohare airport to the Hyatt Ohare Hotel?

Yes maam

Yes the bus comes every 30minutes it's got Hyatt on it

Yes

Yes, Make sure you board the one for Hyatt Regency in Rosemont.

There is a shuttle for both the Hyatt O'Hare and the Hyatt Regency O'Hare, just make sure you get on the right one! The one for the Regency is blue, the other one I believe is red/maroon and white. Both stop for pickups at the shuttle/bus stop at O'Hare.