Dick,

A picture of what you are talking about would probably help a lot but let me offer my two tin pennies worth anyway.

Sounds like 'BOW' would be similar to 'Ground lead', in other words a non-standard term or phrase used by personnel to describe a characteristic that may be better described using a different term, such as camber or sweep.  Camber for vertical distortion and sweep for an horizontal distortion. 

Now, you aren't going to find this in AISC or AWS code documents or specifications.  More than likely it would be dealt with best in a company QC Manual and/or specifications for a product. 

When you say boom tubes I think of log stackers, CAT equipment with clamping jaws, backhoes, trackhoes, extendable boom cranes, etc.  Many of these have a built in camber to compensate for loads.  But, an extendable boom would have to be straight with no load in order to extend and retract.  So, a specification that called out the tolerances makes a great deal of sense.

The question becomes one of 'how much' is allowable?  I'm afraid only the manufacturer and their engineers can really determine that.  Forget about rules of thumb, and industry standards.  They don't mean a thing when dealing with issues like this. 

He Is In Control, Have a Great Day,  Brent