If they find a illegal immigrant on public streets, they can be detained, but still cannot enter a private residence (even if occupied by an illegal immigrant) as it would violate the 4th amendment.
Even an actual judicial arrest warrant doesn't (legally) allow them to enter private party on suspicion that the target might be there. Search is a separate thing from seizure, and you need a judicial search warrant to search a private residence or the non-public areas of a business for a person, no matter what authority you might have to arrest them should you find them.
Criminals are also frequently gullible.
And bail agents are fairly notorious as a group for having a less than scrupulous attention to legal restrictions.
So, a mix of things, really.