road trip, should I bring my bike??

I'm heading out on a climbing road trip in a couple of weeks, places that I'm hitting up for climbing are:

El Paso (Hueco Tanks), Tx
Tucson, Az
maybe Flagstaff, Az
Joshua Tree, Ca
Bishop, Ca
Yosemite, Ca
Red Rocks, Nv

And then back through Utah and Colorado before heading up to Ontario. While this trip will be primarly for rock climbing, my bike will be pretty pissed if I go to Moab without her.

My problem is that I will be driving and I'd keep my bike locked up in the car, but I'll be leaving the car alone for full days while I'm climbing and I'm terrified about someone breaking into my car.

So my question: is there enough biking around these place that I'll be climbing at to warrent bringing a bike with me? (want to spend most of my time at J-Tree and Hueco, and perhaps a chunk at Red Rocks). Or should I just wait till I get to Moab and just rent (or borrow, if I meet up with people) a bike there?