Without seeing the scene it's hard to know with absolute certainty what you could have done differently, but for me the first 'red flag' in your question was your statement that there was a bright background. That doesn't make it impossible to get good steam, but it makes it a lot more difficult... Especially in uncontrolled lighting situations like the one you seem to be describing and even more-so if the steam was faint as you describe. The other thing to note is that on a scale of 'easy' to 'impossible,' photographing steam is a moderately difficult assignment, even under perfectly controlled studio conditions.

My thoughts would be these:

1. Change the camera position in order to get a dark background. This one is tough to work around... steam is light and wispy with no defined edges, thus it is very easy for it to get lost with a bright background.
2. Use a fill flash positioned somewhere between 90 and 135 degrees perpendicular to the camera (It's a variable. Your light won't necessarily be in the same position shoot-to-shoot... Depending on how active the steam is, it may not even be in the same position shot-to-shot). This should brighten up the steam considerably with the goal being to separate it from the background.
3. Shoot a ton of pictures. Steam is one of those things that you end up taking lot of frames and hoping you get a couple that are great... There's certainly an element of luck or 'happy accidents' that play a part in capturing great shots of steam.

If you're looking for some practice, I'd recommend buying some incense sticks and working on getting great shots of that... You'll walk away from that practice with a much better idea of where you're going to need to place your lights in order to give yourself the best chance for getting a few 'winners.'