If she'll mail the letter for me on her way home that will save me the trip.
If she'll put the letter in the mail for me on her way back that will save me the trouble of going to the post box.
“save you the trip” に似ている “save you the trouble” の表現もあります。例えば “New instant infrared thermometers save you the trouble of having to get a child to sit still for several minutes to take their temperature.” (新しい一瞬で終わる赤外の体温計で体温を計るために子供を数分じっとさせる手間が省きます。)