How long does noro survive outside the body?

My concern is my phone. Say I'm at the gym touching all kinds of things like machines and barbells after god knows how many people have touch them. I then check my phone after getting a text. So now whatever germs I have on my fingers may be transferred to my phone. I always wash my hands vigorously after the gym, but if I go and touch my phone again, could I still have any noro on the phone? Washing my phone with bleach every time I touch it when out and about is just too impractical. Are there likely to be noro viruses that survive long enough to end up on my phone which my fingers my pick up?

It's not extremely likely you'll find norovirus just randomly at the gym! Most surfaces there are easily cleanable and washed often.

As for your question, a little research revealed an answer.

Norovirus will remain viable longer on clean surfaces (no chemicals to destroy it), cool temperatures, and no sunlight exposure. The article I read said 2 weeks in a normal indoor environment it is possible to still be infectious.

This article was talking about mainly a location which had an accidental severe contamination event; NOT one or two virus particles on a phone. So probably your phone is safe!