The published minimum connecting time (MCT) is 90 mins, so you are well within that.
BA will certainly check you and your bags in for the connecting flight; just have the details to hand when you check-in at IAD. I've done this before on separate PNRs.
Of course, there is a chance that your inbound flight might be delayed and in this case BA have no contractual obligation to protect you. Worst case scenario is that you have to buy a new one-way to BHD for the later flight. Insurance ?
The only way to be certain is to change your existing ticket to add the domestic leg, but that would likely result in a change fee.
The Heathrow transfer guide is here
http://www.heathrowairport.com/heath...nal-1-domestic
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