Not that she doesn't like the tug on string and ball on string--she plays with them well enough, although she grabs the string more than anything else (I heard somewhere here that she'll outgrow this?).

But I've noticed that she seems to like biting anything that's dangling off of me, or on me, rather than what I'm holding. So if I'm playing with the tug or ball with her, she loses interest after sometime (although this has been improving over the past few weeks), but if I start to run, to gain more movement from the tug, she gets really excited and goes for ME instead of the tug. Like, my pant legs, although I've had some success wrapping a burlap around my arm and letting her aim for that. She REALLY jumps. And then she holds on. If I play with a tug, I cannot pull very hard or she lets go, but if she does this with something attached to me I can literally swing her around and not have her bothered.

Sometimes also, if I play with the tug and she's feels like it, she goes for my hand or arm instead.

She is 3 months old.

My question is, how can I direct her to the tug, or is this okay? This bitework training is mostly for my own education than anything else; if she won't work out for Schutzhund I don't mind. It's not like I can drive to any clubs at the moment anyway...

It sounds like you are putting more movement into your body (like when you said you were running), therefore your dog is looking at you as the prey item instead of the tug.

Try putting more movement into the prey item, and less movement in your body.

Guess so. I'll try to cut down on my exercise...

So her grabbing the string instead of the Kong/ball/tug is okay for now? I use hemp string which I guess feels good to her teeth--should I use something else?

Kay,
Slow down, as mentioned above you have turned into the prey item. Your dog bites the string because it can't get the ball. The prey item has too much movement and the pup isn't able to target the ball or tug. So goes for something moving slower(the string). Use the resources in the training articles section and get the video. You may want to try using a buggy whip and tie the ball or tug on the end.