Opinion: B vs Walking

I was Tryndamere in one game. My team started at top right, had LeBlanc, Caitlyn, Blitzcrank, and Garen, while the other team had Sona, Yasuo, Teemo, Thresh, and Varus.

During a team fight near the river, my health was low, so I used R and went to the nearest bush (right behind our mid turret). Meanwhile the fight moved down the river towards the dragon. At that point, since the fight was moving away, I decided to B. (You can see my position in the Champion Kills section of the match history. Varus got that kill)

Seven seconds later, Caitlyn ran towards me with the whole enemy team behind her from the river. At that point I knew she was not going to make it. They have a fed Sona for movement speed and all. Anyhow while I was telling her to not to come my way (1 second left) and make a right towards the bot lane instead, she lured the whole team directly into my bush, and I died with 0.5 seconds left in the countdown.

According to Caitlyn, that was on me because "I was B-ing too close to the fight" and "I should have walked back to base". Meanwhile I was certain Caitlyn would've died regardless of which route to take and she should've gone the other direction to cut losses. (Caitlyn was the other death by Varus next to my bush).

Opinions?