Originally Posted by
corporate-wage-slave
You should get your boarding pass either online or in Shannon. When you arrive in Terminal 5, off your SNN flight and bus transfer, there is a visual check of your boarding pass and a quick scan of the passport by BA staff just as you enter the T5 building (Flight Connections). This is done for ESTA / APIS reasons. Then this is repeated at the gate just before boarding. In your shoes I'd check-on online. Any luggage won't need rechecking if it is one ticketed booking.
Good advice from
c-w-s re: getting your BP ahead of arriving at LHR.
IMHO, once you are at LHR in transit it would take a serious paperwork/booking discrepancy for any BA staff member to make the decision to off-load you (and your luggage). It's much easier to turn pax away before check-in than once they (and their luggage) are "in the system".