Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Phoenix to Bristol as you normally would.
For a flight from Phoenix to Bristol, you will be flying into Bristol. Bristol (BRS) is just 7.4 mi from the center of the city. Bristol is the only Bristol airport and it handles 0 inbound flights from Phoenix per day. 1 airline has flights to Bristol from Phoenix on a regular basis.
Due to the rapidly changing circumstances due to COVID-19, airlines like Delta flying from Phoenix to Bristol have implemented new flexible change policies.
Yes, there are multiple flights from Phoenix to Bristol for under $1,400. The cheapest flight booked recently is on Lufthansa for just $1,306, but on average you can expect to pay $1,306.