The Hawks displaced long-time leaders Dartford on Saturday, taking full advantage of the Darts’ shock home defeat to struggling Poole Town.
Bradbury’s men won 1-0 at Oxford City and are now a point clear at the top of the table.
Crucially, they also have two games in hand still and the Hawks are now favourites to secure back-to-back League titles.
Bradbury told BBC Radio Solent: “We’ve got to make it last. It’s important where we are at the end of the season, not where we are now.
“We’re not getting carried away. We’re proud of where we are at the moment but there will be twists and turns.
“We’re in a commanding position but we’ve got to make the most of it. The two games in hand we’ve got - Wealdstone and Truro away - are difficult.
“Two points a game until the end of the season will be the aim and if we can do that then I think we’ll win the League.”
Photo by Martyn White
For more news, reaction and action from across the National League, like us on Facebook and follow us on Twitter and Instagram.