Following a delayed start 34 overs were bowled, in which Gloucestershire moved on from 31-0 overnight to 120-1.
After a long delay, the two teams came back out under the lights at 21:00 BST, but the visitors remained untroubled.
After 21 from Chris Dent, Bancroft got to 69 with Will Tavare still there on 43 as the visitors closed on 150-1.
Having begun the day with fears of following on, on his 50th first-class appearance, Tavare's unbroken stand of 88 with Australian Bancroft, who passed his previous season's best of 53, leaves Gloucestershire just 59 runs short of that initial target.
But against a Sussex side who are unbeaten in seven matches with Gloucestershire, there is little hope of the visitors improving on their record of just two wins from 18 visits to Hove.
Cameron Bancroft made only his second County Championship half-century of the season as Gloucestershire reached 150-1 against Sussex at rain-hit Hove.