Originally Posted by
corporate-wage-slave
That makes sense for HBO travellers, but the OP wants to check in bags, and there is a risk that they won't be able to re-check the bags in AMS until 4 hours to departure.
I am not sure who handles AY at AMS, but if they AY happens to have another flight anywhere between 11 and 2, the TO should have no problem dropping off their bags after arriving on BA.
Edit: I'm wrong, see cws's comment below!