1) on reserved tickets NO : some division apply restrictions on unreserved ticket but not all. The retiring rooms at mysore are outsourced to private agency (sandesh group of hotels). You don't need a ticket to stay there as its outsourced.
2) Depends on once liking and comfort. A bus takes between 2:45 - 3:30 hrs depending on the type you board(there are more than 5 types). Trains, between 2 - 3:30 again depending on type.