The backups on the bridge going east are sort of a hit or miss event. I did it yesterday and had no problem, a bit slow for about a quarter of a mile but nothing frustrating. I have only had one time where it was really backed up in, say, 6 or 7 drives. Generally, I cross that area at around noon, on weekdays, if timing has anything to do about it. OTOH, I have seen horrible backups on the eastbound lanes when driving westbound. Going south to 98 never seemed to make much sense due to the damage in Pensacola/Navarre so never tried it. I think there is a northbound alternate, but cannot recollect how that works. Seemed awfully far out of the way if you are coming in from I10.
Make sure you have plenty of gas before you hit the bridge, I tell people visiting.