The cash-strapped Bulls, who were docked six points for entering administration in midweek and lost both a prospective buyer and their third high-profile player in a month just afterwards, scored four tries as they beat another side tipped for relegation, London Broncos, 25-12.
Nick Scruton was the latest to leave, his departure echoing that of Jarrod Sammut before the win over Wakefield.
Cummins, whose side remain bottom of the table two points adrift, said: "There's no question about the spirit among the players.
"We have to show character all the time and found a way to get win which means we could be less than a week away from getting back to even keel (zero points).
"The stuff that those players have had to put up with - just when we think were getting somewhere then something else happens.
"And I can't blame Nick Scruton - he was a mess when he came to tell me that he'd decided to go to Wakefield.
"But it put us in that situation again whereby we were a couple of days before the game and found that one of our players wasn't going to be there."
Anthony Mullally, on loan from Huddersfield, and Academy products Tom Olbison and James Donaldson had big games and Cummins continued: "He's (Mullally) done well for us and that's exactly what we needed with losing 'Scruts'.
"He's filled a hole, has got a big engine and we are able to give him Super League experience which will benefit him, benefit us and benefit Huddersfield in the long term.
"It's the only way and we have young men building their careers like James Donaldson and Tom Olbison, they have been immense and what the club has invested in them is now paying off."
London coach Tony Rea knows about assembling a competitive side amid uncertainty and turmoil and was not helped at Odsal by the loss of three outside backs before half-time.
Jordan Atkins pulled out before the game with a suspected broken hand sustained the day before, while Tonga full-back Nesiasi Mataitonga (hanstring) and Mason Caton-Brown (concussion) were both helped off in the early stages.
"It was an outrageously gutsy performance, given where we are at," said Rae, who put together virtually an entire team in the past three months.
"Plenty of teams would have got beaten by 50 out there today.
"We had no subs left, lost three outside backs and had four injuries during the first half, so it was a big ask and a huge challenge in adversity.
"It was great to still be in it at the back end of the game and at one point I thought we were going to get the job done."
Bradford scored twice in the first half through former Broncos half-back Luke Gale and Adam Sidlow before Thomas Minns replied for London.
Danny Addy and James Cunningham traded tries after the break before a Gale drop goal eased the Bulls' nerves and a last-minute Olbison try sealed the victory.
Jamie Foster converted all four Bulls tries while Josh Drinkwater tagged on both goals for the visitors.
- Sports & Recreation
- Nick Scruton
- London Broncos
- Tom Olbison