Bachman tallied twice in a span of a 71 seconds to cut the lead to 6-3 as part of a five-goal Midd-West run.
Sarah Talabiska broke the six-all tie with 2:37 left in the first half and then scored less than a minute later to give Lewisburg an 8-6 lead at halftime.
"Getting out to a 4-0 lead was really important to us," Lewisburg head coach Janelle Groff said. "Winning the draws was a key to winning the game as it allowed us to control the pace."
Lewisburg won 11 draws to 2 for Midd-West, while the Green Dragons also won the ground-ball game (9-6).
Talabiska finished with six points, while Rachel Murphy, Lisa Steinhubl, Hanna Gotoff and Jessica Penn added single goals for the Green Dragons.
Midd-West (2-1) cut the lead to 8-7 on a goal from Katie Kreider that came off a rebound three minutes into the second half. Talabiska gave the Green Dragons a two-goal lead five minutes later before Julie Hurst got the Mustangs back to within a goal at 9-8 with 16 minutes left in regulation. Hurst had two goals, while her sister Nicole added one.
The Mustangs had their chances in the second half but hit two post and one cross-bar with shots.
Ashley Bilger had a four-goal game, scoring two of Lewisburg's final three.
Midd-West goalie Mikayla Freed made 10 saves.