Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Southampton to Bristol as you normally would.
Flights from Southampton to Bristol lean towards being more expensive in June. Prices are generally better when you fly from Southampton to Bristol in October, with the cheapest ticket starting at £74.
This flight path from Southampton Eastleigh to Bristol was viewed by 14 users in the past month. Keep an eye out for changes in search interest prior to high and low season.