An alternative to the potential observers example is don't do that in the first place. Make something happen in the scene the player can have the character respond to rather than do it "off-screen." The PC is spotted by a nefarious-looking sort who then darts off in the other direction. What do you do? Maybe they run after them. Maybe they don't. Maybe they do and catch him. Maybe they don't. But that solves your "metagaming" concern right there. DMs are almost always the cause of their own problems with "metagaming" and frequently their chosen solutions just make it worse (or shift the "metagaming" somewhere else).
This I'm personally not willing to do, because it conflicts with other aspects of my DMing style. The immediate results of being observed are going to depend mostly on the type of surveillance the bridge was under, and that in turn depends on the available resources and priorities of the king's spies.
So whether the bridge is under surveillance by agents mixed in the crowd, a guy with a spyglass, rat familiars, scrying, a 6th level Eagle-Totem Barbarian, or nothing at all will depend on my high-level world-building decisions (possibly made in advance, possibly made on the fly if I'm improvising). And I don't emphasize the DM-as-referee style, so I absolutely will take into account what I think will be fun for the players when figuring out the resources and priorities of the king's spies.
But I won't make high-level world building decisions to accommodate the mechanical resolution of a particular check. If I determine that the king's spies are a bunch of Druids, you can bet that a failed stealth check on the part of the PC is likely to lead to a wildshaped mosquito trying to tag along on the PC's clothing (yes, the PC will have an opportunity to notice). As a consequence, I'm definitely going to ask for the PC's stealth check up front, to avoid letting the PC know whether or not they were observed.
I fully recognize that my preference here is a result of my emphasis on the strategic level of gameplay. My games slant heavily towards Combat-as-War, so it is important to me that how and whether the bridge is under surveillance be consistent with my high-level world-building decisions regarding the king's spies' methods and resources. Your suggested approach may work quite well for games that don't share my idiosyncratic style preferences.
