It takes me about 35-45 minutes from there on most days.  

Take AL Hwy 182 that becomes FL 292 (called Perdido Key Dr, Sorrento Road, Gulf Breeze Hwy and finally Barrancas Ave) all the way into Pensacola and take a right on West Main St (just across the railroad track). That will take you to the US Hwy 98 Pensacola Bay Bridge (3 mile). Stay on US Hwy 98 till you get through Gulf Breeze and turn right onto FL Hwy 399 (Gulf Breeze Pkwy). The Bob Sykes bridge is right around the curve going toward Pensacola Beach. 

It's in two pieces and to access the southern half you need to go thru the toll booth.

Hope this helps!

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Woooo Hoooo! The Gulf State Park Pier opened up @ 11am July 20, 2009