This is plenty of time. If this is booked as a single ticket (it sounds as if it is), then your bags should be checked through. I would confirm this at check-in, though, as BA has a reputation for being a bit uncooperative in this regard (though I have never had a problem). You may also need to show your bag tags to the service desk on the other side of security at LHR, so they can 'find' your bag, but this may only be for separate ticket connections.
Otherwise, do as StarWorld says and follow the signs to the bus. The trains are landside, so you would need to clear immigration (not recommended, again assuming that your bags are checked through) for that. My guess is that your gate-to-gate time will be less than an hour.
As to the plane... I do think it is more uncomfortable than many other options, but it isn't the end of the world.