However, with the home nations each preparing for autumn internationals next month, both sides are missing a number of senior players.
Ulster confirmed yesterday that just three of their 14 Ireland squad members (Stephen Ferris, Craig Gilroy and Paul Marshall) would be available for the match, while Edinburgh Rugby welcome the return of four of their 12 players out on international duty.
Bradley said: "There's a lot to play for in what is effectively a mini-series of games coming up during the internationals.
"This is the squad we'll be asking to win games and, because of the changes imposed on both Ulster and Edinburgh by availability, the game is up for grabs for whichever 15 players takes hold of it.
"It's a great challenge for us. We've had a disappointing run of late and have spoken about how great a place it would be to end that run, so we're approaching the game in a very positive frame of mind.
"Ravenhill has become a bit of a fortress so it's a daunting task. They will be well supported and are on an unbeaten run but, from our point of view, we're desperate to get a win, we've trained well this week and are very focussed and driven to do a job in Ulster."
Of the 12 Edinburgh Rugby players selected for Scotland's EMC Test matches next month, Grant Gilchrist (lock), Stuart McInally (number 8) and Lee Jones (wing) return to the starting line-up, while prop Allan Jacobsen continues his recovery from a hamstring injury on the bench.
With Greig Laidlaw unavailable, Sean Cox assumes the captaincy, and starts on the blind-side of a new-look back-row, with open-side Roddy Grant and McInally.
Robert McAlpine steps into the second-row berth vacated by Cox to partner former age-grade international colleague, Gilchrist, while the front-row trio of John Yapp, Andy Titterrell and Willem Nel remains unchanged.
Despite the international obligations, the club's back three has a familiar feel as Jones lines up along side this season's ever-present full-back Greig Tonks and wing Tom Brown.
John Houston returns to partner inbound centre James King, who starts his first match of the season, and stand-off Gregor Hunter replaces the injured Harry Leonard (groin) to partner Chris Leck, whose composed performance against Scarlets is rewarded with a recall.
Other noteworthy inclusions see new lock Izak van der Westhuizen available to make his debut from the bench, while Hamish Watson (back-row) and Sep Visser (wing/full-back) could also make their first competitive appearances of the season.
Bradley added: "There are couple of players who have been knocking at the door for selection and this game gives them an opportunity to prove that they're a serious contender for matches going forward. If they produce wins for the club, then there's no reason why they can't stay in the side.
"Izak [van der Westhuizen] is a quality player and a pretty robust character in terms of his ball carrying.
"He moves well as we saw in training yesterday though it was a tough day for him after stepping off the plane, into a medical, and then out to training.
"He's enthusiastic and desperate to play, and will bring an added a physical dimension to our game, which we're looking forward seeing."
Edinburgh Rugby team to play Ulster at Ravenhill on Friday 2 November (kick-off 7.05pm) RaboDirect PRO12 round eight - live on BBC ALBA.
15 Greig Tonks
14 Lee Jones
13 John Houston
12 James King
11 Tom Brown
10 Gregor Hunter
9 Chris Leck
1 John Yapp
2 Andy Titterrell
3 Willem Nel
4 Grant Gilchrist
5 Robert McAlpine
6 Sean Cox CAPTAIN
7 Roddy Grant
8 Stuart McInally
Substitutes
16 Alun Walker
17 Allan Jacobsen
18 Lewis Niven
19 Izak van der Westhuizen
20 Hamish Watson
21 Richie Rees
22 Dougie Fife
23 Sep Visser
Not available through injury: Ben Atiga (hamstring/knee), Dimitri Basilaia (knee), Ben Cairns (knee) Jamie Farndale (leg fracture), Steven Lawrie (knee), Harry Leonard (groin) Perry Parker (hip), Netani Talei (knee), Steven Turnbull (knee).
On international duty: Geoff Cross, David Denton, Ross Ford, Nick De Luca, Greig Laidlaw, Ross Rennie, Matt Scott, Tim Visser
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