Bruce has submitted two bids for the Dundee United and Scotland left-back, 20, without success and is now preparing to hit the £2m mark in an attempt to convince the United chairman Stephen Thompson to sanction a sale.
The Barclays Premier League club signed Robert Snodgrass, the Scotland midfielder, from Norwich City for more than £6m earlier this summer and have strengthened their squad by bringing in Jake Livermore from Tottenham Hotspur and Tom Ince from Blackpool.
Thompson, who has banked £3m from Sporting Lisbon for Ryan Gauld, will no doubt be interested in Bruce's opinions on investing in homegrown talent as he continues to play hardball with all parties interested in his players.
"If I can buy in our market, I always will," said Bruce. "You pay a premium for a young British player and that's what we've done. There's the problem in our game. You can get a player from overseas for half the price.
"We've got a 22-year-old, a 24-year-old and a 26-year-old. It's cost us more money, but I would expect that.
"You know what you're going to get. There will come a time when I know what I'm going to get from the foreign market and, hopefully, we can get that set up in the next 12 months. To really progress in the foreign market, the next stage for the club is to have people working for us scouring Germany, Italy, Spain and France."
Thompson made it clear he will not sell players unless he believes the deal makes sense for his club and is determined to secure the right price for Robertson, with other suitors such as Everton and Queen's Park Rangers understood to be interested, having scouted him over the course of last season.
Bruce has money available, though, with Hull getting ready for a first excursion into Europe in the Europa League's third qualifying round on July 31.
"We're as well-equipped as we've ever been," said Bruce. "It's an excellent squad. We haven't got a lot of numbers, but I'm really content with what we've done. Ideally, we'd still like another two or three in, especially with what we've got ahead in Europe.
"If we can get a left-back in and a centre-back, maybe we'll look for a middle of midfield player, too, or someone that can do a bit of everything."