Bradbury, who enjoyed two playing spells with Pompey, leads Cherries into battle against Saints for the first league meeting between the clubs at Dean Court since 1960.
Southampton's fall from grace has seen them become League One foes for Cherries this season, with both clubs in the mix to join Portsmouth in the Championship.
Victory for Cherries in front of a full house at Dean Court would see them open a six-point gap on their neighbours, while Saints would leapfrog Bradbury's men with a win.
Bradbury told the Daily Echo: Southampton have always been a massive club with a rich tradition and history. They have had some great players down the years and their facilities are excellent. They were in the Premier League when I first started playing and Pompey were in the league below. Times have changed and them and us are both trying to join Pompey now.
Providing it is good, rivalry among local clubs is healthy. Supporters want bragging rights when the clubs meet and we want three points to keep them off our tails. It would be great to play in the Championship week in, week out. That's where we want to be and players want to play these games every week.
There is going to be a bit more pressure on our lads than normal for a home game because there is going to be a full house. But if the lads want to play at a higher level, then they have to deal with the pressure because it is all part of the game. The atmosphere is going to be electric and we are playing a team in form. It should be a good yardstick to see where we are.
Bradbury will also be hoping Cherries can bounce back after he presided over his first defeat as a manager at Exeter in midweek. The setback in Devon ended an impressive 10-match unbeaten start for Bradbury and assistant Steve Fletcher.
Everyone was disappointed, said Bradbury. But I have told the players to let it hurt them but not let it affect them. We have told them to use it as ammunition for the next game and to show people what a good side we are. The lads don't need picking up with a game like this on the horizon.
Southampton are a great side and are just behind us in the table. It has got all the makings of being a great game. They have got a couple of games in hand on us and have got to play us as well. I would rather be in our position to be honest.
We have been through a lot in the past few years and it is great for everyone at the club to be involved in a top-of-the-table clash. We should all feel very proud of what we have done.
Bradbury said he was optimistic striker Michael Symes (groin) would be fit to keep his place, while defender Shaun Cooper is today due to resume training after illness forced him to miss the midweek trip to Exeter.