Something similar was asked before, but this is a different way to ask it and maybe it is time for some updates.
LEGO has released sets of Technic parts at various points in time. Some sets have been available under LEGO's Education line, but these and a couple of others were released in normal retail channels in 2003:
I don't see any indication that LEGO will still sell you these directly at this point.
For your purposes you probably are better off finding a Technic set that is within your price range and going with that. Having instructions for building one or two things will help spark the imagination. If you can't get more Technic for a birthday or other holiday that's coming up, you can always encourage them to take apart the model from instructions and try something else. Building from a set also means you end up with a nice selection of parts. You're not going to end up with 10x too many of one thing and none of something else that might be more useful. Almost any set is going to have a useful selection of parts for building a variety of things.
Amazon has a number of similar things:
If you want to get more of specific kinds of parts in "bulk" this is will remain a viable way to do that.
You can find LEGO by the pound on ebay and at LEGO stores not run by the LEGO group itself. We have a place here that you can go in and there are tables with parts to pick through. They have tons of Technics, bricks, plates, minifig parts, Bionicle bits, etc. You can get a bag of whatever you want for $20-$80 depending on how big the bag is.
Vendors of bulk LEGO tend to set up shop at LEGO shows and conventions. You might discover that there are some unofficial LEGO shops in your area already. Since they don't have the advertising dollars of the official stores they might be in your town and you've missed it.
bricklink is the ultimate ebay replacement and encyclopedic reference for LEGO sets and parts. If you want 200 of a part in one color or 1 each of 200 different parts, this is the place to make it happen.
I haven't done any bulk purchases on ebay or Amazon, but otherwise I've had good luck with LEGO sets, bulk from stores, and bricklink.