Here’s the thing. If you’re going with the whole alien hunter thing, then you’re probably looking at the police and military. Remember, Groom Lake was an Air Force Base, and that is military.
The short answer is anyone that singles her out and she catches paying attention to her, and that’s about as good as it’s going to get. Unless she knows specific tells with the agents hunting her, like, say, that they’re all aliens themselves, and have some distinguishing characteristic, then there’s that, but otherwise, she’s just going to have to rely on her own paranoia.
As I understand it (and keep in mind, this is a little out of my forte); the basic advice with protective details is to scan the area, and if anyone sticks out in your mind, keep an eye on them. But, as simple as that is, it’s hardly foolproof. Over time, more details of what you’re looking for specifically will get filled in, This is just the old “one of these things doesn’t belong” game with assassins and attempted murder.
Also, “disguise” makes me think of Groucho Marx glasses. Realistically, in a situation like this, a disguise would probably be something as simple as jeans and a t-shirt, with maybe a jacket or work shirt if it’s appropriate.
This is also going to get into a protagonist/antagonist bent, so, I’m going to start with the assumption that your conspiracy agents are the bad guys.
In order to be effective, they need to be able to escalate. They need to have the ability to act openly if the situation really warrants it. Otherwise it will just be too easy to outmaneuver them. In the real world, hunting and killing anything bipedal is generally frowned upon by the police, and any antagonist that can be completely neutralized by dialing 911 is a poor foe (at least in this context.) This means, setting them up like the fake emergency call in the Bourne films would be an amazingly fast way to get rid of them, and it would work reliably.
So, your antagonists need to actually be affiliated with either the police, military, or both. If it’s a conspiracy outside of the government, they need to have pull inside the police. These need to be people that really can call the cops for backup, and possibly (depending on what they’re hunting) the national guard or marines.
If it is a conspiracy, then their front line agents will probably be ex-law enforcement or ex-military. These are the kinds of people that have the necessary skills, the background, and the outlook for the job. This also means, they’ll be very hard to spot, because you’re not looking a specific set of characteristics, you’re having to look for a lot of possible tells.
If the group is actually your protagonists, and the situation is a little different. In this case, your agents will look a lot more like resistance fighters. Ex-law enforcement and military are still preferred, but they might have to take whatever they can get.
They’re also going to need to be very careful. One slip up could mean their entire operation is in jeopardy, and the police are a serious treat to their ability to function.
In a case like this, agents could be potentially impossible to spot. The easiest way would be to look for the same faces popping up. These guys don’t have a large staff to pull from, so they can’t afford to rotate their surveillance. They also probably couldn’t afford to track someone “just because they might be a problem later”, again, they don’t have the numbers to do that. So if they’re stalking your character, it’s because they’re planning to neutralize her, soon.
You can run groups like this as antagonists, but it’s not easy. Hunter: The Reckoning is written from the perspective of the rag-tag monster hunters being the protagonists, but the books could give you some ideas for using them as antagonists. While we’re on the subject, Hunter: First Contact is specifically built around running these two types of groups against each other, and it does offer some good suggestions, even if it is geared for a world where Vampires control the police, and the werewolves are ecoterrorists.
First Wave was a… let’s call it quirky series about a lone alien hunter trying to save the world. Cade Foster wouldn’t make for a good antagonist, but if you can track the show down, it might give you some ideas. Also, the aliens in the setting are interesting, and Roger Cross’ work as an enforcer for the aliens is very memorable. Fair warning, the first season DVD set is obscenely expensive, and I don’t think SyFy’s released the others, so this might not be an example you can actually use.
I’d be remiss if I didn’t mention V. Either the original series from the early 80s or the reboot a couple years ago. I’m not a fan of the former, and I haven’t seen the remake. But, it is the urexample of a resistance cell fighting against an alien invasion. This is pretty much the opposite of what you’re wanting to do, but it might help.
By the same token, I’m not a fan of Earth: Final Conflict, but the show was about resistance fighters hiding inside, and working to subvert aliens who came to earth openly. It’s at its best when the aliens are ethically ambiguous, but that gets lost in later seasons, as the aliens become more overtly evil. It probably isn’t exactly what you’re looking for, but for anyone else in the general vicinity.
You can run conspiracies as protagonists, but it’s tricky. Stargate: SG1 is a good example, and The X-Files plays this for both the FBI agents and the conspiracy. The British miniseries Ultraviolet plays a lot like this as well, though they’re hunting vampires, not aliens. If you’re going for more of a comedy bent, the MIB films might not be a bad place to look. The first film in particular, has a wonderfully surreal quality.
This one might not be possible to track down, but The Visitor (1997) was a really interesting series where an alien abductee returns to earth, and is trying to save the world. It’s notable for having two separate groups, a slightly deranged military commander tasked with covering up alien activity, and a cadre of FBI agents. If you can find a copy, this was a really good series.