I'm sure toothpicks would work because I have heard enough people talk about them.
But even though they probably do... I would go with the bamboo because of better tensile strength.
For myself, I use pieces of popsicle sticks. The wood seems stronger on them than toothpick wood. The last thing you need is to put something in there... and then have the screw 'spin' again when you're tightening it up.
And if you happen to use my method... cut a piece of the stick to completely fill in the hole and then just break it (or cut it) off flush if you've cut it too long. It's not that hard to get the screw started again in the middle. Sometimes I'll use an ice pick to make a little pilot hole but usually you won't have to do this.
And maybe all popsicle sticks are not created equal??... the ones I have are fairly rigid and strong and don't need glue for strength, although I guess it wouldn't hurt if you wanted to do this too.