I run my bike on the Utah county bike trails frequently, along the Jordan river and up Provo canyon. I see signs that say that firearms are prohibited, but from what I understand, these are bogus. Am I mistaken?
I can take a photo of one of these signs if it'd help.
I would say they are bogus for those legally carrying. Your permit gives you permission to carry anywhere that is not specifically forbidden by law, and county property is not forbidden. If you can carry while talking a walk down the sidewalk, you should be able to carry on county bike trails. Heck, you can carry in National Forest's, so why not these trails?
As always, IANAL, take my opinion for what you paid for it! If in doubt, call the Sheriffs Office.