Keep in mind that manufacturers recommend that you scuff-up the primer if it is outside of the recoat/top-coat window. This is applies to a number of popular DTM, catalyzed and self-etching primers.
For example, Summit Racing DTM primer (what I'll be using for my TJ in just a few short weeks), says the following:
DTM Epoxy Primer may be topcoated for up to four days without requiring the surface to be abraded or any additional prep. After four days, epoxy primer surface MUST be abraded to ensure proper adhesion prior to topcoating.
Their flat etching primer states the following:
May be recoated in 30 minutes. If sanding is desired, SUM-SWSP200_-12 may be sanded in 60 minutes. Do not wet sand. Scuff sand with 320 grit or finer sandpaper after 24 hours. Repriming is not required
I spent a handful of summer working at a body shop and for us the base primer coat was always really meant for surface/corrosion protection, which I suspect is the same case as your bumper. If you care how it looks, at least in the long term, I would scuff it with a soft Scotch-Brite pad and then give a good wipe down with solvent/reducer of choice. If you're just going to bolt it on and bang it up on the rocks, then I wouldn't bother and would just slap some Rustoleum on it and call it a day.