Travel from Portree to Edinburgh

Can you define "best"- cheapest, fastest, most scenic, least changes?

Are you travelling on transit, or driving? If on transit, do you prefer trains (where that option exists) or are you up for a long (6 hour or more) bus ride?

Any which way, driving or transit, it is most of a day's journey.

There is no direct public transport route. As isn31c says if you're needing to do the journey by public transport then it will be a combination of bus routes or bus plus train. As an example you could take the Citylink Bus to Glasgow and then the train to Edinburgh. Or the Citylink bus to Inverness and then the train to Edinburgh. There are various combinations of these routes that would be possible depending on the times of the bus from Portree and the train connections. The simplest way is by car, but one way rentals from Skye would not be possible as the only car rentals places on the island are local garages who would have no way to get the car back from Edinburgh.

I want to travel from Edinburgh to Mallaig by train, take the ferry to Rum for a couple days, then back to Mallaig to take another ferry to Armadale on Skye. Then I’m looking for some kind of public transportation to Portree. We’d like to spend a couple days on Skye using an on-island tour, then find public transportation back to Edinburgh, stopping in Inverness, and maybe other places along the way.

Armadale to Portree is not easy on public transport. There is one bus a day in the morning and it's very early as it's basically the school bus. You will likely have to get a taxi from Armadale to Portree which you would need to book in advance to meet the ferry. Tours around the island are available but the only one I could recommend with any confidence are Skye Jeep Tours as I don't have any personal experience of any other tours.

To get back to Inverness you'd need to take the City Link Bus and from Inverness you could take a bus or train to Edinburgh, breaking your journey in various places depending on what you are interested in seeing on the way there.

Right,

So assuming your entire trip is less than 8 days you want a Scottish Grand Tour Rail Ticket- https://www.scotrail.co.uk/tickets/combined-tickets-travel-passes/scottish-grand-tour

Day 1 (Sunday, Tuesday, Thursday, Friday or Saturday)- Train Edinburgh- Glasgow Queen Street (switch trains)- Mallaig- Overnight
Day 2 (Monday, Wednesday, Friday, Saturday or Sunday)- Mallaig to Rum ferry [on a Saturday only you can do Edinburgh to Rum in a day]
Day 3 Rum
Day 4 Rum- Mallaig- there is never a same day Rum-Armadale- Portree ferry/bus connection
Day 5- Mallaig to Armadale to Portree on the once a day bus at 1035 from Armadale, Monday to Friday only
Day 6 and 7-Skye
Day 8- Citylink bus Portree to Kyle of Lochalsh, Train to Inverness, switch trains, Train INV-EDI

You can't overnight in INV as you are out of days, but may have an hour or two between trains.

This works from Edinburgh therefore on a Sunday, Thursday, Friday or Saturday.

You need to book your stay on Rum early as there is very little choice.

You can only connect Rum to Mallaig to Armadale on a Saturday and Sunday- with no transport forward to Portree.

You would need to see if connections are any better going the other way round the circle (Skye then Rum) but I doubt it..