With the injury curse continuing to bite – seven players who featured at Dings the week before were unavailable – the visitors struck early as Tom Mills went over on the right.
Dan Cole added to a James Apperley effort before Max Marshall mauled over for Rams.
A Cole penalty made it 15-5 at the break, but the hosts made a perfect start to the second period as Axel Kalling-Smith crossed, Ross McKay with the extras.
Ben Atkins was harshly sin-binned for the home side before Ioan Parry went over.
But two quick-fire converted tries via Kalling-Smith and Ant Marris put the Berkshire side 26-20 up.
A second yellow card, this time to Marshall, proved pivotal with scores from Austin Pope and Mathis Dehauteur, plus a Cole conversion, giving Bishop’s an eight-point lead.
The Rams scrum took complete control late on and James Baker gave his side hope, but they ended falling just short.
‘Good energy’ from returning players
Director of Rugby Seb said: “It was a good game and we felt we were good for the win, but it wasn’t to be and credit to Stortford.
“I was pleased with the lads. We had lots of changes with debutants and guys coming back from injury, but there was great fight, determination and there was some decent stuff.
“I was very pleased with the way we started the second half. We got on the front foot and Ben Atkins and Mikey Duda added good energy (on their first appearances of the season).
“Axel and Paddy Harris were also excellent and it’s nice to have them back.”
He continued: “There are a couple of areas we need to work on, and we have to put games to bed when we hold the advantage.
“Our guys felt arguably a bit hard done by with the yellow cards, but they did their best to put it right themselves.
“We must do our best to take any decisions out of the game and start winning rugby matches.”
‘Injuries create opportunities’
Rams have used a remarkable 31 players in taking six points from their opening three fixtures, but Seb said it will benefit the squad long-term.
He revealed: “We’ve come up against an excellent Sale side, a dangerous Dings and now Stortford.
“We’ve picked up some bonus-points which is good, and I’m happy with the depth we’re building.
“The young players who have come in have done well, but it will take time to build cohesion and how we’re looking to play as a team.
“You get these phases and you have to turn it into a positive. Isaac came in and he did very well, Theo at 15 the same.
“They’ll have naïve moments and get things wrong, but they’ve got tenacity and were in the game.
“Every injury you just have to say ‘who’s the next cab off the rank and how are they going to go?’ Sometimes you find gems, so there’s no point crying over spilled milk.
“Results are definitely coming.”
Rams host Rosslyn Park on Saturday (3pm). For tickets and lunch bookings, click here