The township is named in honor of Solomon Bastress of Jersey Shore, who was a former member of the legislature and an associate judge.

They migrated to the area beginning in 1837 under the leadership of the Jesuit missionary Father Nicholas Steinbacher.

Immaculate Conception parish and school stand today as a reminder of the German Catholic heritage of the residents of Bastress Township.

Pennsylvania Route 654 passes through the center of the township, leading northeast 10 miles (16 km) to Williamsport and south 2 miles (3 km) to its terminus at Pennsylvania Route 44 west of Collomsville in Limestone Township.

The crest of Bald Eagle Mountain forms the township's northern border.

Two streams, Big Run in the west and Bender Run in the east, rise in Bastress Township and flow north, cutting through Bald Eagle Mountain to reach the West Branch Susquehanna River.

Bear Pen Hollow is a ravine in the southeast corner of Bastress Township which drains east to Mosquito Creek, which also flows north to the West Branch of the Susquehanna.