Gotta say Bret, with maybe both the IC and WWF titles. If he had previous attempts, it would likely be with Perfect on the house show loop, I'd guess and those don't count.
I didn't look into 1985-86, but here's what I found on Bret's previous attempts:
Prior to winning the IC belt -
WWF @ Binghamton, NY - Broome County Arena - June 22, 1988 (6,000)
Bret Hart (w/ Jim Neidhart) fought WWF IC Champion the Honkytonk Man (w/ Jimmy Hart) to a double count-out at 8:05 when both men began brawling on the floor
WWF @ Turin, Italy - April 7, 1989
WWF IC Champion Rick Rude pinned Bret Hart
WWF @ Amarillo, TX - Civic Center - July 2, 1990
Bret Hart (sub. for Brutus Beefcake) vs. WWF IC Champion Mr. Perfect
WWF @ Providence, RI - Civic Center - April 26, 1991 (6,000)
Bret Hart defeated WWF IC Champion Mr. Perfect via count-out
WWF @ Rochester, NY - April 27, 1991 (7,100)
Bret Hart defeated WWF IC Champion Mr. Perfect via count-out
WWF @ Orlando, FL - Arena - April 28, 1991 (6,700)
Bret Hart defeated WWF IC Champion Mr. Perfect via count-out
WWF @ Wheeling, WV - Civic Center - June 10, 1991 (5,500)
WWF IC Champion Mr. Perfect fought Bret Hart to a 20-minute time-limit draw
Prior to winning the WWF title -
WWF @ Kiel, Germany - Ostseehalle - September 27, 1992 (6,000)
WWF World Champion Ric Flair defeated Bret Hart via count-out at 34:33
WWF @ Birmingham, England - NEC - September 29, 1992 (12,000; sell out)
WWF World Champion Ric Flair defeated Bret Hart via count-out at 25:16
WWF @ Aschaffenburg, Germany - Unterfrankenhalle - October 2, 1992 (4,500)
WWF World Champion Ric Flair defeated Bret Hart via count-out
WWF @ Frankfurt, Germany - Fest Halle - October 3, 1992
WWF World Champion Ric Flair defeated Bret Hart via count-out
WWF @ Los Angeles, CA - Sports Arena - October 10, 1992 (7,300)
Bret Hart defeated WWF World Champion Ric Flair via disqualification at 23:45 when Flair pushed the referee
WWF @ Red Deer, Alberta - October 11, 1992
Bret Hart defeated WWF World Champion Ric Flair via disqualification
source:
www.thehistoryofwwe.com