Having just done something similar (sleeper from London to Fort William), I can't recommend it enough CL.
Although it's more travelling, getting on the Sleeper at Euston, is, IMO, the only way to do it. That way you can get the full experience; the excitement of walking along the (very long) train to find your carriage is huge.
As for destination, I agree with Jane; get off somewhere quiet(ish). The trip on the FW train as it crosses Rannoch Moor is amazing but FW can be a bit dispiriting if the weather is bad. We spent Sunday wandering around in the rain and wind before checking out a couple of bars. Neither of them were great. I should add that we had neither bikes nor walking gear although, even if we had, either activity would have been grim. Cycling FW to Inverness is on my list of things to do before I die. I've just ticked off the sleeper
I'm fonder of Aviemore as a poor weather destination although it can also be bleak.
If it helps with the decision, the Scotrail info was adamant that bikes wouldn't be transferred by staff to the FW train. You could try asking the steward to do it for you; the guy on our trip was very helpful. Maybe bung him a fiver ?