I timed it myself and put a timer exactly by the frame at the start from when the "fight" screen starts to fade in, to the exact moment the victory screen starts to show up. Its a 34 millisecond difference the the current wr.

Btw I streamed this if you want more proof than this I never joined any party: (timestamp 10:20 for the alleged wr)

Mod Note 1: Retimed (Start Frame: 2147, End Frame: 4407, FPS: 60, Total Time: 0:37.667)

Mod Note 2: Since it is impossible to join Bridge Solos while being in a party, running /p info is technically not necessary for Bridge Solos speedruns. No further proof required.