Despite being deprived of some internationals last week Edinburgh overcame the Ospreys 23-13, and Bradley wants to build on that success with his side sitting eighth in the RaboDirect PRO12 standings.
Greig Laidlaw will be returning at stand-off, while Matt Scott and Nick de Luca will continue their partnership in midfield and Tim Visser will take up his place on the wing.
And Bradley admitted he had no hesitation in bringing his stars back, saying: "In the past, we might not have included guys like them in our plans and given them a rest.
"But this is such a vital match for us in terms of building momentum and continuing the good work of last weekend - the win against the Ospreys was very important.
"It was an excellent performance and the forwards in particular stood up and took the game to the opposition to make sure of the success.
"It is only right that we should put out as strong a side as possible for the Connacht trip.
"Connacht always like to take on the Scottish teams at home because they think we are a soft touch. We must rid them of that attitude by winning."
63x46.png){kind=logo}