Bates, now 4-0 on the season, will face UMass Boston in the tournament championship at 3 p.m. on Saturday.
Stockwell has eight career double-doubles, with two this season.
Bates built a quick 7-0 lead, but John Jay came back to take a 17-16 lead with 8:18 to play in the first half. It was the only time the Bobcats trailed, as Bates took a 27-22 lead at halftime and pulled away early in the second half.
Zak Rayadded 13 points for the Bobcats, while Brian Gerrity and Brian Wholey both added 10 points apiece.
Bates held a 42-30 rebound advantage and a +10 turnover ratio over John Jay, which fell to 0-3. Thirteen players scored for Bates, a season high for the Bobcats.