Tammy Abraham joined the Robins in a season-long loan deal this summer.
Ashton told the Bristol Post: “At the end of last season, Lee went to Chelsea's training ground and presented to Michael Emenalo [Chelsea's technical director], while I went to Stamford Bridge and met Roman Abramovich's board of directors.
"They had tried these arrangements with English clubs before and, in their words, they hadn't worked. They gave me a list of clubs they would not do business with.
"I asked them to give us Tammy for the season and then judge us on what we do, not what we say. I told them we would show them what we could do and then build a long-term relationship.
"We then did the deal with Chelsea and sorted all of the finances, which were far from straightforward. Then we had to wait for (Antonio) Conte."