Leah Galton, Millie Turner, Jess Sigsworth and Tobin Heath were all on the scoresheet for Casey Stoneys side while Ebony Salmon scored Bristols goal.
The Manchester United manager was pleased her team claimed another win, saying: “It is nice to go in top at the break but we can only control what we can, and we did that today by getting the points.”
Tanya Oxtobys team were still looking for their first win of the campaign and started the match brightly when Salmon chipped the ball, which drifted wide.
United had chances of their own but were made to work hard for them, as Jackie Groenen and Ona Batlle were denied.
The hosts took the lead in the 26th minute when Galton scored a thunderbolt from outside the area and United doubled their advantage just before the break when Turner rose highest from a Heath corner.
In the second half, Sigsworth fired home from 12 yards to add a third, before Galton scored her second – another stunner from outside the area.