Another, more solid way of handling it would be to invoke the aspect for effect. This could then simply prevent the attacker from attacking or create a block (either at the GM's discretion) that would remain until the aspect was no longer applicable (I.E. the PC does something that would invalidate the aspect or the enemy counter-maneuvers).
I wasn't certain Invoking for Effect worked that way... but it does give me an idea.
I was looking at the bonus from cover as something that should always be there. But, narratively speaking, the bonus only really needs to be there when it needs to be there (Ooooh... Zen Gaming). In other words, you don't need that +2 bonus to defense if the enemy misses. Only does good if the enemy hits (at the very least, you're reducing the stress you take by 2 points).
Also, a "Cover" aspect doesn't have to be invoked to the benefit of the player... It could compel the enemy instead!
So, here's what I'm looking at...
Step 1: Maneuver to generate a "defensive" temporary aspect on yourself (It doesn't even have to be cover-based, though that's our current example). Presuming you roll well enough, it's sticky and hangs around until someone takes a counter-maneuver to get rid of it.
Step 2: Wait until an enemy attack hits (we'd be a little lenient with the "must be used immediately" part of a free tag), then use your free tag to boost your defense or compel the enemy into missing.
Step 3: Use Fate Points to gain additional benefits throughout the scene, or re-maneuver to get another free tag.
I think that would pretty well to emulate the guy who's crouching behind cover, but occasionally popping out to take shots... As opposed to someone who completely under cover and staying there.