2020: two-year-old season

Bay Bridge began his racing career in a seven furlong novice race (for horses with no more than two previous wins) on soft ground at Yarmouth Racecourse on 12 October when he started at odds of 10/1 and finished third to Marrakech Moon, beaten five and three quarter lengths by the winner.^[6] On his only other start of the year he finished fourth in a similar event on the synthetic polytrack surface at Kempton Park Racecourse in November.

2021: three-year-old season

On 7 April Bay Bridge began his second season in a novice race over ten furlongs on Tapeta at Newcastle Racecourse when he was ridden by P. J. McDonald and started at odds 9/4. He took the lead a furlong out and accelerated away from his four opponents to win "comfortably" by five lengths.^[7] In May the colt started 11/4 favourite for the London Gold Cup, a handicap race over the same distance at Newbury Racecourse which saw him assigned a weight of 122 pounds. Ridden by Ryan Moore he raced towards the rear in the early stages before going to the front two furlongs from the finish and stayed on well to come home four lengths clear of the runner-up King Frankel.^[8] He was then aimed at the King Edward VII Stakes at Royal Ascot but was forced to miss the race owing to a foot abscess.^[9]

After a break of almost five months Bay Bridge returned for a ten furlong all-aged handicap at York Racecourse when he was ridden by Richard Kingscote and started favourite under top weight of 132 pounds. He was restrained towards the rear of the field by Kingscote before producing a strong late run which saw him gain the advantage in the closing stages and win by half a length from the six-year-old gelding Platinumcard.^[10] On 30 October the colt was stepped up in class to contest the Listed James Seymour Stakes at Newmarket Racecourse in which he was partnered by Moore and went off the 6/5 favourite in a five-runner field which included the dual Canadian International Stakes winner Desert Encounter. He raced in second place before moving up to join the front-running Majestic Dawn approaching the final furlong and got the better of a sustained struggle to win by half a length.^[11] Michael Stoute commented "Bay Bridge had a little niggle in the summer that kept him off, but his attitude was good there today. He's a professional horse with a good mind and I think he'll stay a mile and a half."^[12]

2022: four-year-old season

Bay Bridge's third campaign began with a move up in class for the Group 3 Brigadier Gerard Stakes over ten furlongs at Sandown Park on 26 May. With Moore in the saddle he went off the 7/4 second favourite behind the Gordon Richards Stakes winner Mostahdaf in a five-runner field which also included Addeybb, Lord Glitters and Dubai Future. He settled towards the rear as Addeybb set the pace before making a forward move in the last quarter mile and taking the lead a furlong out. Bay Bridge drew right away in the closing stages and won in "impressive" style by five lengths.^[13] After the race James Wigan said "He's such a big, strong boy. We rather thought in the paddock that he looked as though he might need the race but we've always thought a lot of him and Sir Michael has always been very complimentary about him... I'd be inclined to stick to a mile and quarter at present. He's beaten some good horses in a good race today. Ryan said he showed a great turn of foot and it's very exciting."^[14] In the 5 June edition of the World's Best Racehorse Rankings Bay Bridge, despite never having contested a Group 1 race, was rated the fifth-best horse in the world behind Baaeed, Life Is Good, Nature Strip and Speaker's Corner.^[15]