Mitzi Steady was walking with her grandmother on Lansdown Lane in the city when she was hit by the truck.
In a letter to her daughter read out during the service, her mother said: "We only had four years with you but they were the best years of our lives."
An investigation into the crash, in which four people died, is continuing.
Mitzi's coffin was painted in the style of a scene from the Disney movie Frozen.
White flowers spelling out her name accompanied the coffin and the song Do You Want to Build a Snowman? was sung by Melody Makers - the abbey's choir for children aged from six to 11.
In the letter read out during the service, Emmajade Steady said: "How can it be that there will be no more memories?
"You were just becoming a young girl. So smart, so open and free.
"I want to come home to you throwing yourself at me again. I want to give you your special milk on your cereal and ask 'what shall we do today?'"
She told the congregation of "rough and tumble games" Mitzi played with her brother Eric and described how excited her daughter was for her first sleepover.
Speaking ahead of the service her family asked for donations be made to the road safety charity Brake instead of flowers.
A campaign launched after Mitzi's death has raised more than Â£15,000
The three others killed in the crash on 9 February were Phil Allen, 52, and Stephen Vaughan, 34, from Swansea, and Robert Parker, 59, of Cwmbran.
Mitzi's grandmother remains critically ill in hospital in Bristol's Southmead Hospital.
Two men arrested in connection with the crash have been bailed by police.
Hundreds of people have joined family and friends at Bath Abbey for the funeral of a four-year-old girl killed in a tipper truck crash.