Bradley, formerly director of rugby at the Galway club, said: "It was very important that we got a win last weekend, we badly needed to get a 'W' on the board. It's been great for our confidence as we've prepared for Saturday's game.
"Connacht target the arrival of the visiting Scottish sides because they feel they've an excellent chance of winning those games.
"We've talked about that a lot at training this week as something we have to change.
"In the past we might not have brought the Scotland players straight back in and maybe given them the weekend off after the Tests, but it's vital that we build on the momentum from the Ospreys match, and have picked a strong side with the aim of doing just that."
Coming back into the fold are captain Greig Laidlaw at stand-off; Matt Scott and Nick De Luca continue their club and country partnership in midfield, Tim Visser steps back on to the wing and David Denton packs down on the blind-side of the scrum.
Denton's return sees Sean Cox move back to his favoured position at lock to partner Perry Parker who impressed in his first start against Ospreys last week.
Hooker Andy Titterrell replaces the injured Ross Ford (shoulder) and Allan Jacobsen is offered the chance to impress from the outset at loose-head prop.
The remainder of the back-line is unchanged with Greig Tonks (full-back), Tom Brown (wing) and Richie Rees (scrum-half) all earning reselection.
Edinburgh Rugby team to play Connacht at the Sportsground (kick-off 5pm)
RaboDirect PRO12 round 10
15 Greig Tonks
14 Tom Brown
13 Nick De Luca
12 Matt Scott
11 Tim Visser
10 Greig Laidlaw CAPTAIN
9 Richie Rees
1 Allan Jacobsen
2 Andy Titterrell
3 Willem Nel
4 Perry Parker
5 Sean Cox
6 David Denton
7 Roddy Grant
8 Stuart McInally
Substitutes
16 Alun Walker
17 John Yapp
18 Lewis Niven
19 Robert McAlpine
20 Izak van der Westhuizen
21 Chris Leck
22 Gregor Hunter
23 Dougie Fife
Absent through injury: Ben Atiga (knee), Ben Cairns (knee), Dimitri Basilaia (knee), Jamie Farndale (leg), Ross Ford (shoulder), Piers Francis (leg), Lee Jones (groin), James King (leg), Steven Lawrie (knee), Ross Rennie (shoulder), Netani Talei (knee), Steven Turnbull (knee).
Players released to RBS Premiership clubs: Alex Black (Edinburgh Accies), Michael Penn (Heriot's), Sep Visser (Boroughmuir)