Bonus points from the losses to Munster and Leinster keep the club mid table ahead of their trip south to face the tenth-placed Welshmen, whose round one win over Zebre is their only success in the last eight games in the competition.
However, despite their slow start, the Dragons have a formidable record against the men from Murrayfield, celebrating a home and away double last season, and keeping their visitors from an away win since 2006.
"This is a critical match," said Bradley.
"I've been satisfied with our performances so far this season but we must continue to improve if we are to fulfil our ambitions of making the play-offs, and that means winning away from home.
"There are no easy contests in this division, especially when you're on the road, and Dragons are notoriously difficult to break down.
"Their defensive approach is quick and aggressive and puts a lot of pressure on the opposition, so the fundamentals of our game will have to be very well executed.
"We will have to be sharp and clinical to make the most of any manufactured or opportunistic chances. It will be very tough game."
Bradley's team features seven changes to the side that started last week's narrow loss to Leinster at the RDS, with Scotland trio Ross Rennie, Allan Jacobsen and top try scorer Tim Visser returning to the front-line.
Outbound are their international colleagues Greig Laidlaw, Ross Ford and Matt Scott, who have each been rested for the match, with Bradley calling on quality replacements in their stead.
The front-row swaps one British Lion for another, as Andy Titterrell makes his first competitive start at hooker and former All Black centre Ben Atiga returns from a hip strain to operate at inside-centre alongside Nick De Luca.
At stand-off, 20 year-old Harry Leonard has the chance to recapture the form that saw him start three of last season's Heineken Cup pool matches, while lock Robert McAlpine completes the pack alongside Sean Cox, who takes on the captaincy from Laidlaw.
Edinburgh Rugby team to play Dragons at Rodney Parade tomorrow (Friday 28 September, kick-off 7pm)
15 Greig Tonks
14 Tom Brown
13 Nick De Luca
12 Ben Atiga
11 Tim Visser
10 Harry Leonard
9 Richie Rees
1 Allan Jacobsen
2 Andy Titterrell
3 Geoff Cross
4 Robert McAlpine
5 Sean Cox CAPTAIN
6 Stuart McInally
7 Ross Rennie
8 Netani Talei
Substitutes
16 Alun Walker
17 John Yapp
18 Lewis Niven
19 Dimitri Basilaia
20 Roddy Grant
21 Chris Leck
22 John Houston
23 Dougie Fife
Unavailable though injury: Ben Cairns (knee), David Denton (thigh), Gregor Hunter (peck strain), Steven Lawrie (knee), Perry Parker (ankle), Matt Scott (hand), Steven Turnbull (knee)
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