For the most part, enslavers with large operations would know that an enslaved person has gone missing fairly quickly. Plantations are not modern factories or office spaces, but they did run on regular routines where one would expect people to show up at the right place in about the right time day in and day out. The major exceptions would be Sundays and Christmas, which enslaved people could have mostly to themselves. The customary understanding was that they might be abroad on such occasions visiting friends and family owned by others.

But an absent slave isn't necessarily a runaway in the minds of enslavers, so there's usually a delay on taking action. Most slaves who stole themselves do not seem to have intended to get to the North and freedom. Instead, they wanted to claim a few days for themselves away from the misery to visit friends and family elsewhere in the area or just to have some alone time. Then they would come back, act properly apologetic, and hope for a light punishment. This happens often enough that enslavers have a stereotype that black people just don't know what they're doing and temporary absconding is a kind of adolescent rebellion that infantilized blacks can't mature past. Racism explains everything. :(

In the absence of some indication that an enslaved person really does intend to be gone for good, or some sort of general tension in the white community about the security of slavery, usually a few days would go by before a self-stealing slave goes from "missing but coming back soon" to "runaway, might be headed North." It's impossible to put a firm number on this, the one of the first reactions that's easily visible to us in the record is when the enslaver puts out an ad in the paper telling people to be on the lookout. These often point to the expectation that the enslaved have gone to visit or expect to rely on friends and relations for help. For example:

Runaway from the subscriber, his Negro men. JOHN and TOBEY. [...] They were bought from Mr. James Surles, of Cumberland county, and will probably be lurking in that neighborhood. Tobey has a wife at Mr. Richard Bird's, in Johnston County. Fifty Dollars for either, or one hundred Dollars for both, will be paid for their apprehension and delivery to the subscriber, or for their confinement in any Jail in the State, so that he can get them. An additional sum of One Hundred Dollars will be paid for the conviction of any person harboring the above Negroes.

This is a pretty typical ad, from which I omitted the customary physical description. There's a reward offered and enough to get a guess as to who the accused are, then instructions on where they might be headed. Unfortunately it doesn't also tell us how long they've been gone for. I hoped I might find an example of an ad that clearly lists the time, but for the most part they're short. Here are a pair from the Gazette of the United-States for June 30, 1792:

RUN AWAY from the subscriber, living in Kent County, and State of Maryland, on the Sunday the 27th May last, a NEGRO MAN, named HARK

That's a month later, which seems like a long time. It looks like it was copied from a Chestertown paper of June 4, which is much more plausible. (The 1791 date has got to be a printer's error.) The generalizations I've seen in the surveys usually allow a few days to a week before fugitive hunting gets under way in earnest. Sending people out to ask the neighbors might have happened before that, since it's free.

The ad immediately below is something else, though. A Robert Pearce, of Head Sassafras, offered thirty dollars and "reasonable charges" for the return of Phil. Phil absconded in February and it doesn't seem that news hit the Gazette until June 16. There's no way Pearce, or whoever had direct charge of his enslaved people, only noticed then. I suspect that in Phil's case, Pearce gave it the customary week or so and this is an ad he's rerunning.