The pair enjoyed a week-long romance before her gangster boyfriend warned
him off.
Jillian told Scotland's Daily Record newspaper: "Brad had just shot
'Interview with the Vampire' in Britain with Tom Cruise and had come to
Glasgow to check out the architecture.
"Someone in the bar said he'd been in some cult movies, then I recognised
him from 'Thelma and Louise'.
"Brad spoke to me a few times during the day. And at closing time we decided
to head on elsewhere.
"He was just a lovely guy, who wasn't pushy or full of himself. I felt
really flattered because he could have chosen anyone but he went for me."
Jillian had a boyfriend at the time - local bad boy Hugh O'Donnell - but
says meeting Brad "just happened" and she was "just having a laugh".
The pair spent time together in Brad's hotel room - but Jillian insists they
did not have sex.
She said: "We had a bath together and he massaged my legs and feet. Brad
asked in a really gentlemanly way if we could make love but I said no.
"Although we ended up in bed, I insisted on keeping my knickers on. We just
kissed and cuddled."
However, the romance met an abrupt end when Hugh found out, and told Brad to
keep away - or else.
In 2000 - when Brad was in the UK for the premiere of 'Snatch' - he
reportedly told a Scottish reporter he had "left a lovely girl behind" in
Glasgow.
Brad said: "We were making out and getting on well and I didn't know there
was a problem until a guy came up and asked if I knew who I was messing
with. I got out of there and really felt quite glad to be alive!"