There are quite a few Serviced Apartments in Mysore.
You could consider Urban Oasis Mysore. I have visited their Bangalore facility (near MS Ramaiah Hospital off New BEL Road) and found the place neat and tidy. Looked like they follow some standards for housekeeping. I have not had the chance to visit their Mysore unit, but looking at their Bangalore premises, I think the unit in Mysore would be as good as Bangalore.
Specifically request and check availability for fully equipped kitchen since you intend to cook your own food during your stay at Mysore.
Hope the above was helpful and wish you a pleasant stay at Mysore.