Month to Month Business stay away from home

Hi, I am self employed and was living away from home out of my state from August-November paying month to month rent in cash to another individual. Since I was only staying in this state to work and do business, am I able to deduct a portion or all of the lodging expenses and how do I prove it since I paid the other person cash? I was told I could deduct my hotels/stays on business travel but How long can someone stay in another state and work to where it is still considered a deductable travel expense?