Badshotomen kinda stole my thunder. If the cat is after you, it will be from behind. The only way you will see it is if you surprise it, not the other way around. And mountain lions should scare the crap out of you. They are the only wildlife that will routinely intentionally hunt a human.
Story from a hunting rag a few years back - a father/son were out hunting deer, saw something down by a river. Dad put the scope on it, and the cat looked back at him. Dad and son skeedaddled back to the pickup and came back next day with help. The cat had followed them back to the pickup. The now much larger group swept through the area for some time, and ended up back at the pickups without seeing the cat. Then they saw the tracks following their trail as they swept - the cat had tracked them the whole way and was likely watching them at the moment they realized it.
Object Lesson - Cats attack from behind.
Actually the small airhorns with the handle bar mount are a great idea.
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It should more than suffice for a sub 100 pound cat.
Just what we want to hear on the trails, especially the Maah-dah-Hey, airhorns. Doubt seriously they would work on a cat, other than to resound like a dinner "bell".
And just what kind of pussy cat do you have in FL? Sub-100 pounds? If it is a young'un or sick and dying, maybe it's sub-100 pounds. Most of the healthy ones up here are well over 100 pounds, with the males heading toward 200.
In event of cougar? Fall backwards off the bike and you'll have a sore butt, but still have time to draw whatever weapom you choose (this being plan A).
One more time - cats will attack from behind, they are stalkers.
Another story from a hunting rag - a couple of turkey hunters were sitting on the ground with their backs against some trees calling the birds. One heard a faint rustle from behind, glanced back, and barely had time to swing the shotgun muzzle and pull the trigger before the cat dropped dead in his lap. Object Lesson - When you sound like prey, you are prey. Oh, yeah, and cats attack from behind.
A couple of ideas, DR. 1 - Backpack with hydration is a great idea, especially if you can find something to ride high over the back of the neck. And made of Kevlar maybe?
2 - keep weapons (yes, plural) on your body, not on the bike. Maybe start with a shoulder holster, plus belt carry, cross-draw or better yet weak hand in case your strong is is, you know, busy being fed to the cat?. As for the Bond derringer, better than nothing, especially if you're up against the wussy cats in FQ's neighborhood. Up here? .45 ACP or 9mm HP only, and lots of them. And maybe a Bowie knife - you know, just in case?
3 - Check with the rangers before you ride to see if any cats have been seen recently. Cats cover a lot of ground so this isn't foolproof, so one could just show up, but will at least let you know if one was in the area for sure. Watch for sign as you ride, tracks, scat on the trail, etc. Absence of other wildlife too, although hikers/bikers will spook much of the wildlife.
4 - Don't ride alone and keep those behind you in your mirrors, don't let anyone get trailed too far behind - they are the prey of choice. Safety in numbers.