The accident happened in Wide Lane, Morley on Wednesday, September 19.
The 13-year-old schoolboy had alighted from the bus, which had stopped across the road from his home, when he was hit by a truck as he went to cross the road.
Lindsay Spencer was travelling on the bus when she saw the accident and ran to help.
Other schoolchildren on the bus had dashed over to his home to get his mother, Jo Easton, from her home nearby.
Mother-of-two Ms Spencer said: "I am incredibly proud of how calm Tom's mum remained throughout. She was beside herself with fear but kept herself together to help her son.
"Tom was laid on the floor with his mum breathing into his mouth while I compressed his chest."
Ms Spencer, 39, had been on her way to work when the tragedy struck.
Paramedics arrived at the scene, taking over from the two women, and Thomas was taken to hospital.
While there, his family had to watch on as doctors fought for his life as he underwent countless procedures.
The family kept Ms Spencer up to date with what was going on, all the while praying for him to survive.
She said: "At one point I was told his chances of survival were 60:40. But he had been in intensive care, had fluid on his brain and been put in a coma.
"I couldn't help thinking that, knowing how long he was not breathing for, that his chances of complete recovery must be very slim.
"What has happened has haunted me ever since. I remember every detail but it doesn't seem real. Like a bad dream.
"The next thing I heard, the family had decided to switch off his life support machine. I feel so sad that he has died.
"I have been told his mum is pleased that they have decided to save others by donating his organs. She is an incredibly brave woman.
"Even though we didn't save him we did absolutely everything we could to save him. We did our best."