"Running Left" is a useful strategy, but probably not the best one over all in my opinion. Depending on where you are on the structure, the oncoming traffic of rolling barrels, and how you time your run, you may not always be able to beat the wild barrel to the left.
As a very strong alternative (or perhaps as a new "plan A"), try positioning Jumpman exactly underneath the wild barrel just at the moment that it bounces off of the girder directly overhead. If you do it correctly, the wild barrel will always bounce severely to the right and out of harm's way. It's virtually impossible to be hit by it in this position.
A couple of points about this tactic:
If you are a bit late getting into position while running right to left, or if you have drifted a bit too far to the left at the moment the wild barrel bounces off of the girder directly overhead, it will end up bouncing to the left instead of sharply to the right. Often times this bounce to the left will occur at a relatively shallow angle, coming close to hitting Jumpman and perhaps just missing him off to the left side. BUT, when this occurs, the wild barrel will then bounce off of the girder THAT YOU ARE STANDING ON, and bounce severely to the right -- and it CAN and WILL hit you in the foot! Anticipate this and JUMP for style points (and survival).
The other important point is that if you happen to be standing under the wild barrel as it changes into a Level 5 wild barrel, then of course it will drop onto your head instead of bouncing severely to the right. As you begin playing bottom hammer games this is actually something that you have to actively keep track of, watch out for, and avoid. However, if you are literally running boards towards a killscreen, you should never have to deal with internal difficulty transitions anyway (although you might run into this in a top hammer only game while using the top hammer).
Anyway, just keep playing and eventually over time you will get more and more used to dealing with these. It may also be helpful to remember what these L3 wild barrels are programmed to do and what they MUST do algorithmically. Basically, at the moment of each bounce off of EVERY girder, the wild barrel will look to see if Jumpman is positioned somewhere to its left, in which case it will bounce left, or if he is positioned somewhere to its right, in which case it will bounce right. If it bounces right, it will generally bounce at a sharper angle (and hence it will be travelling faster since vertical speed / acceleration is basically fixed). Armed with this knowledge, one of the biggest things to do that will improve your play in these situations is to simply stay calm when you recognize that a L3 wild barrel has entered the screen and immediately begin aggressively seeking a solution instead of panicking and "hoping" to survive.
And just so you know, we all still get hit by these occasionally . . . RESTART!