A count of several thousand last-minute absentee and provisional ballots Thursday widened Bilbray's second-place lead over millionaire challenger Eric Roach to more than 1,000 votes.
Only 880 votes separated the two Republicans following Tuesday's special election.
Bilbray had 20,880 votes or 15 percent of the updated total, while Roach had 19,827 votes or 14 percent.
Roach made a concession call to Bilbray and left a congratulatory voicemail message, said Roach spokesman Stan Devereux.
County officials reported that some 1,000 last-minute votes still remain to be counted. Final election results are expected to be released Friday.
Busby, a local school board member, had 44 percent of the vote to lead all 18 candidates.
The winner of the June runoff will serve the eight months remaining in Cunningham's unfinished term — and immediately begin campaigning for November.
Cunningham resigned late last year after pleading guilty to accepting $2.4 million in bribes from defense contractors. He was sentenced in March to more than eight years in prison.
Bilbray, a surfer, one-time lifeguard and San Diego-area native, held a San Diego seat south of Cunningham's wealthy coastal district from 1995 to 2000.