Looking for a facility which offers respite care for my 99 year old mom.

My husband is hospice pt living at home with me but he goes to a 5 day respite facility every 60 days and covered by medicare

Select a facility that is convenient for you.
Stop in or call (I would stop in) and ask if they can do a Respite Stay.
You may need to plan in advance as there are forms that would have to be completed. Medical history as well as a doctor's confirmation that she is in "good health". In some states a TB skin test may be needed, although this can also be done with a blood test. (If you opt for a skin test some areas require two tests about a week apart if I recall my test.)
Most of the facilities will do a Respite because they figure if you do decide on placing mom in the future you will select them since you and mom are familiar with the facility.
Now if mom is eligible for Hospice they cover about a week of Respite each year. This is covered/paid for by Medicare/Medicaid. (If she is not on Hospice the payment for Respite would be out of pocket) the kicker is...if the Hospice has an In Patient Unit that is probably where they would place mom otherwise she would be placed in a facility that the Hospice has a presence in and the facility has a bed available for Respite. So you really don't know where she would go.

At 99 years old, your mom may qualify for hospice care and they offer a 5 day respite every now and again in one of their facilities.
And it's all covered 100% under your moms Medicare.

Call the assisted living facilities in your area. Some do provide care for people on a temporary basis.

You can make arrangements for your mom to be cared for while you take a break.

Best wishes to you.