[Spits] tires and tie rods

[Nolan]

By bounce, I take it the tires are out of round.  All tires are out of round 
actually, just some more than others.

You know the cars you sometimes see on the highway with the bouncing wheel? 
The one that makes you think they really need to get their wheels balanced? 
Sometimes those are balanced, and your seeing the bouncing action of a badly 
out of round tire.

Were I in your shoes, I'd take the wheels balanced and out of round and see 
if they feel ok.  If they do, then I'd be good to go.

If they pounded or caused me problems on the interstate (faster spin 
agrevates the problem), then I'd find a shop that understands radial runout 
and has the proper equipment and knowledge to correct the problem.  The 
current shop is correct that many times it can be helped by breaking the 
bead and rotating the tire around the rim, but you don't want to just do it 
blindly.  As well, there is a type of balancing machine that can compensate 
for this.  Pickup trucks with big off road tires often have a problem with 
this, so those shops catering to them often know how to balance a wheel with 
this problem.

I would not shave the tire generally.  That, imo, is a last resort method.