Does a "Bar of Reenlistment" prevent future conscription?

The bar to continued service is a punitive action. He or she is not a candidate for reenlistment or continued service in any Army component. He or she is a candidate for separation if the circumstances that led to the bar to continued service are not overcome.
If a bar to reenlistment is in place when a Soldier ETSs, they will be given an Honorable Discharge. All receipts of both Honorable and a General Discharge Under Honorable Conditions can both be reactivated in time of declared war, since all discharges of that type are subject to inactive reserve status.
You may also be reactivated for crimes committed while in service which are discovered after you are discharged.
If you commit a crime while on any military or federal facility/land while you are still within your 8 year reserve commitment you may be re-activated to active service, but that is rare and usually would not be for petty crime.
Scoure: IAW Army Directive 2016-19, effective 1 October 2016

A Bar to Reenlist merely stops your continued service for the current contract. What is needed to look at is the RE-Code and Separation Code that were given. Plus, since the US doesn't have Conscription, that isn't anything to worry about.

We're not a conscription Army, we have no conscripts, nobody is conscripted. This is like asking "if I throw a football far enough can I get a homerun?".