I can easily get a flight to San Diego, direct from the UK (same as San Fran).
If the riding around there is good, and I can rent a bike I will look into that for sure. If it's dry, I don't mind the cold. 10c/50F is okay - so long as it's dry.

I would much prefer to hire a bike given it would only be a day, maybe 1.5 days tops. Not worth the effort in taking a bike for such little cycling if bike hire is an option. However, if I had my bike and I just went straight to LV (as suggested), I could go a pedal in the mornings before work and at least get some exercise in and then it would be worth having the bike with me. I already have access to the bike box, and the extra bag needed would be covered by the cost of the flight I expense.
I have just looked at Zion National Park - that looks amazing. I've never driven outside of UK, hence my trepidation with hiring a car.