My husband has an FTA are the bailsbounds men or cops allowed to enter my house wihtout my permission?

A Falure To Appear finding by the court usually results in the issue of a Bench Warrant. The officer can enter the primary domicile of the subject or any known location of the subject on the strength of the Bench Warrant for their arrest. They can not enter a suspected location on the strength of the Bench Warrant unless it is the subject’s primary domicile or the homeowner grants permission. They can certainly monitor the possible exits from a suspected location while requesting a magistrate issue a specific warrant for that location.

What a bounty hunter can or can not do is going to be subject to the laws in your state reguarding "independent fugitive apprehension contractors". Generally they are not granted any powers beyond the capture and return of fugitives. Any damages or breaking of the law by a bounty hunter would subject them to the same civil and criminal penalties as any other citizen.

p.s. If your fugitive husband is found in your house when captured, it is possible that you can be arrested and charged for harboring a fugitive. I would highly recommend you cooperate with the police in this circumstance rather than take a trip to jail along with him.