It varies a little from state to state, however, very generally;
A bounty hunter may enter a property or location in which they have a resonable belief the person is present AT THAT TIME. They can not enter a property or location simply because they want to do so using, as an, excuse they believe the person is there, just to force their will. The brandishing of weapons to force entry or your compliance to allow them entry, without that reasonable belief is an unlawful act. If you told them he was in fact in jail at the time, they should have checked that out first before proceeding.
A bounty hunter has the same basic responsibilities under law in this respect as law enforcement officers. In other words they can not abuse their position or imply authority to force compliance simply because they want to do so, they need a reasonable belief. Bounty hunters do not have a "right to search" so they can't just demand entry to check and make sure. On the other hand, if the person flees through your property they can pursue up to a point. That point is the point at which "capture is not imminent" and you tell them to stop and wait for law enforcement, in other words if they spot the guy fleeing through your property and during their pursuit they spend time stopping and searching places on the property and have not captured the person within a short reasonable period of time, then their justification of immediate pursuit is not valid and all they are doing now is searching hoping to find something and that becomes an unreasonable search (in other words they can't spend an hour searching your house or property structures and still try to claim immediate pursuit), and they need to wait for law enforcement to procceed further.
Brandishing weapons like that, and trying to basically force entry or compliance through intimidation like that, created a very dangerous and imminent danger aspect to this. Anytime a weapon is brandished in associated with, or attempted, acts of this nature, an imminent danger aspect is present. The law in all 50 states recognizes an imminent danger aspect in such situations as you have described.
By the way, contrary to the various laws allowing them entry at times, the laws do not remove your rights to self defense or to, in some or most cases, still not allow entry, in such cases. Bounty hunters are not official law enforcement, and an exercise of self defense or refusal to allow entry, is not negated as it is if this were legitimate law enforcement. The laws, generally, only say they may enter (under specific or certain circumstances), but the laws do not say that you must let them enter, for example, if you have a reason to fear imminent danger or know for a truthful fact the person is not there, and in this respect they are not like law enforcement because they have no official standing under which to enforce "warranted search" so in this respect they are like ordinary citizens and when the property owner says wait, stop, or no, in these cases they need to wait, stop, or not do it. However, you also have a right, in all 50 states, to have official law enforcement on the scene as well when they show up, demand entry, or want to proceed - in this case a simple "Wait until the police arrive before you proceed." is sufficient and they are legally bound to wait for that law enforcement to arrive (make sure you actually call the police) before entering or proceeding unless the person attempts to flee and they have a reasonable belief to know that is happening. Most states have laws that require them to contact law enforcement before proceeding in the jurisdiction.
I hope you filed charges at least.