These are the 'official' answers... perhaps you can persuade someone differently, but I doubt it;
if I book the 11:10 flight and miss it will BMI put me on the 16:00?
No, they'll charge you for a new ticket (unless its a flexible ticket in which case no charge). If they are feeling very kindly (which is quite feasible) they may agree to do the change for a fee... but no promises, the change fees are now £50 too, check your ticketing rules.
If I book the 16:00 will they let me change it to the 11:10 on a standby basis?
BD (along with most British airlines?) don't really do standy - again you'd have to pay your £50 fee to get on the earlier flight. You may be able to sweet talk an agent in putting you on an earlier flight - but since you're going to be running to get the earlier flight I doubt you'd have the time...
So; you are really stuck with the long connection unless you put yourself on one ticket - or get a flexible BD ticket on the 11am flight.
Aer Linguis might not be such a bad idea if the times work out better?