How do I bend a wooden edging for a tile counter top?
Unless the wood is rotted or extremely old I doubt its age will have an effect on shaping. Commercial lumber is kiln-dried to a relatively low humidity anyway.

I can think of a couple of options for bending the wood:


Depending on how thin the edging is and how much it's going to curve, you may just be able to bend it by hand as you attach it. If you're talking just a gentle arc along the counter edge I think this would work, but if you want a tight turn at the corner than definitely not. Of course there is a risk of breaking it, so I would only try this if you have a spare piece or don't mind buying another.
Making a homemade steam box is easier than you might think, especially if you're a little handy and only want to bend a few pieces. You just need a closed container that's long enough to hold the item (a PVC pipe, or metal dryer vent, or some scrap plywood assembled in a box), and an electric kettle as the source of the steam. Cut a hole in the side of your box and connect it somehow to the spout or top of your electric kettle. E.g. a piece of garden hose, some tubing, more pipe, etc. Get the whole thing sealed up as best you can with duct tape / caulking. Then just fill up the kettle with water and turn it on! Ideally you would stick a meat thermometer in there so you can tell when the wood reaches an appropriate temperature. Any insulation you can wrap around the outside of the box will make the steaming process faster.
If the piece you want to bend is small, you can actually just stick it in the microwave to soften it up.