If you take the train to Kyle of Lochalsh, walk a short distance to the local Co-op (supermarket) and there is a bus stop there. If you book early the train is about £8 and the local bus is about £3.
The train journey is very scenic and will have quite a few challengers on it.

Tom, if you book now on the Scotrail ticket, a ticket Inverness - Kyle of Lochalsch can be bought for as little as just £10.20 (it will be nearer £27 on the day). You can collect the ticket from Inverness station, but you must use the card you used to buy the ticket to collect it (and have the reference number they give you). The train journey to Kyle of Lochalsch is one of the best in Scotland and although it takes 2.5 hours, it will be a great way of meeting starting the challenge.

As far as your route is concerned, where do you go after Dornie?

You'll need to take the number 11, Jet bus to Inverness Bus Station (make sure you are heading west to Inverness, not east to Nairn) From there, the Citylink 917 bus is the most straight forward route, otherwise there are changes, but they are simple enough and the drivers are (mostly) helpful.
Traveline Scotland, as suggested by Peter, is very useful.

Try to allow yourself some time in Inverness to buy some fuel. There are outdoor shops within walking distance of the bus station. And likely other challengers waiting for the same bus!

I did that journey last year - though getting off a stop earlier at Shiel Bridge.
It’s very easy airport bus to Inverness then the 917 - it’s easiest to book on the city link website.
If you’re getting the evening bus (17.35) it was very full when I used it so pre-booking a ticket would be a good plan.

I’m starting from Dornie this year, but not until Saturday - i’ll Follow your trail.