The deadlock was broken in the tenth minute by the visitors who powered their way over from short range through forward Claire Phelps.
Bristol responded soon after, Tuima took advantage of a misplaced clearance and combined well with Holland who in turn offloaded in the tackle to Phillips to score.
Richmond punished Bristol for an over-throw at the line-out as prop Laura Kapo collected the loose ball and charged over the Bristol line.
Bristol Ladies responded again, this time through winger Lillian Stoeger who sliced through the Richmond backline after a sumptuous backs move.
Richmond bagged another two tries late in the first half through Rebecca Ball and Victoria Britland.
The visitors continued their dominance early in the second half as their captain Rowena Burfield went over to stretch the score to 12-31.
Bristol responded well and finally got the breakthrough they deserved as Lagi Tuima went over for two tries in as many minutes.
Tuima crossed for her first in acres of space out wide after great work from Ellie Mulhearn and Amelia Buckland-Hurry.
She quickly grabbed her second after scooping the ball up from a Richmond mistake and ran in untouched.
Bristol had the wind in their sails but it was a case of too little too late as they succumbed to an valiant opening weekend defeat 24-31 at the hands of Richmond.
Head Coach Kris de Scossa was pleased with his sides performance despite the loss.
“First game of the season, the preparation has gone well. Richmond came out and they played very well,” he said.
“However, you look at your performance, you look at where things didn’t go right and you have to work on it.
“A little lack of cohesion between backs and forwards and certainly some work ons that we are going to identify with that.”
The Bristol Ladies side contained a hand-full of debutants and de Scossa is pleased at how the squad has bonded through pre-season.
He added: “I think they did very very well, in fact, I’m proud of all the players, they took the game on and made the best of it.”
PLAYER OF THE MATCH
Cat McNaney’s dominant defence was a constant throughout the game, she also demonstrated great attacking ability.