How useful? For the spy, it depends on what they’re doing and where they are. For the police? No.
For a spy, local police can be useful, because they’re gathering information as part of their natural activities. If the spy can gain access to that information, then that’s free legwork. They can also be useful as an environmental hazard, for dealing with other spies or criminals. Simply pumping a couple rounds into the street and calling in the gunshots can get the police crawling all over a place. Which is one way to make life very unpleasant for a hostile agent.
That said, a spy has nothing to offer the police. In the US, anything a spy turned up would be inadmissible in a civilian court. Spies, by nature of their job, break the law on a regular basis. After all, this is their job.
Criminal investigations are highly scrutinized as part of the trial. You can’t just sneak in a, “and then a spy broke into his place, stole all this relevant evidence and gave it to us.” You need to establish a clear chain of evidence, from how the police learned of the evidence’s existence, to how they obtained it,and a physical record of everyone who handled it while in department custody.
A spy can break into his place, steal evidence, and then use it blackmail him. That’s different. But that doesn’t help the police at all.
Also, generally speaking, the cops aren’t going to be bribing people. While there is such a thing as a paid informant, these aren’t particularly valuable, and are prone to inventing information to get paid, rather than actually reporting what they see.
But, police, as part of an investigation? They’re not going to offer bribes. Threats and intimidation? Those are still on the table, and if they want to get someone talking they have a lot of coercive options. The courts frown on some of these, but ultimately, they have far cheaper means of getting people to open up than coughing up cash.
They might accept bribes to look the other way, depending on the officers, and where you’re talking about. But, that’s an entirely different situation.
A spy on the other hand, might have to resort to bribery to get the access they need. This is highly contextual, based on exactly who they’re interacting with, and what they’re trying to get. This can even include police. A spy might know a cop, who for $200 will plant drugs on a hostile agent, or give them a copy of the police report for the shooting last night. It really depends on what they need, and who can get them that.
As for mobility? That depends on the spy’s cover and what they’re doing. A spy who spends their days working as a foreign corespondent for a major media network, or as a consultant for a financial NGO could spend a lot of time on the road. One that runs a restaurant downtown, across the street from a foreign embassy might never leave town.
A spy who’s cover is working for the state department as a “security adviser” with diplomatic immunity could be anywhere in the world on any given day.
How much it will cost is also going to be highly dependent on what your spy is doing. Really, there’s no way to generalize this. The monthly expenses of someone who is running a barber shop, with a surveillance suite upstairs is completely inconsistent with someone who has been in 15 different countries in the last 60 days for the WHO.