Good morning. I did a search through the Multiple listing service to see what was availalble through there for you based on your criteria. While there are over 39 homes listed for rent that meet your criteria for bedrooms and bathrooms none were at $1000 or less monthly on rent. The least expensive one I was able to find was $1195.00 a month with a majority of them falling in the $1300 to $1500 a month range.
The other option is to look on craigs list and see if you can find one. But be careful of scams and do not give any information without first seeing the inside of the house.
Coldwell Banker United