Hull's side beat Cornish Pirates 21-7 for their first win of the season
Bristol head coach Paul Hull says the next four games will be a hugely significant part of their season.
They face Bedford on Sunday followed by a trip to Worcester, a home tie against Nottingham and then play London Welsh.
"It's a massive, massive period in the calendar for us because all those teams I think will be in the final play-offs," Hull told BBC Radio Bristol.
"They are the form teams and hopefully we'll be there as well but we need to front up and perform."
Bristol managed their first win of the Championship season just last week when they beat Cornish Pirates 21-7 at the Memorial Stadium.
But arguably they face a tougher challenge this weekend when they take on second-placed Bedford who beat them once last season and ran them close in the other three fixtures.
"I think Bedford's attack is better than Cornish Pirates' so we'll be tested again and we've had some tough games against them over the last 12 months," said Hull.
"They've got some very good half-backs and in Miles Dorrian at fly-half I think they've got one of the best 10s in the league.
"He plays the game close to the line, he's a threat and also he's got a very good passing game.
"It'll be a massive test for us and it'll be interesting to see how we cope with that.
"We want to perform better than we did last week but show the same amount of passion and commitment."
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