Southbound buses operate along their regular route to Bristol Circle and Winston Park Drive, then detour:

northward along Winston Park;
eastward along Plymouth Drive; and then
southward along Winston Churchill Boulevard to North Sheridan Way,
resuming their regular route southward along Winston Churchill.

Northbound buses operate along their regular route to Winston Churchill Boulevard and North Sheridan Way, then detour:

northward along Winston Churchill;
westward along Plymouth Drive;
northward along Winston Park Drive; and then
eastward along Plymouth to Winston Churchill,
resuming their regular route northward along Winston Churchill.

You can see a map of the detour here.

Mississauga Transit has not explained why it is detouring the buses. Oakville Transit buses operating along the 24 South Common Mall and 102 Winston Park routes serve some of the same streets but do not seem to be detouring.