Acraven brings up a very good point. If you're travelling by public transportation, you are at the mercy of the weather. Your lodging may not be within a short walk of the train or bus station, and not every train or bus station has a taxi waiting to meet you. Fortunately, May is one of the driest months in Scotland.
You didn't say whether you were travelling alone, and how long you're going to be in Scotland. Travelling by public transportation can get you just about anywhere in Scotland, but it requires very careful planning. As far as ticketing goes, the Spirit of Scotland rail/bus pass is a good option, but you have to be extremely careful, as you can't travel every day using this pass. For instance, with the 15 day pass, you can only use it on eight out of the 15 days. So if you're travelling from place to place, only staying one day in each place, you'd need two of those passes, which would cover 16 days. Some of the smaller bus companies don't honor the pass, so you'd have to pay individual fares for those journeys. As I said, it requires careful planning.
You may find that some (not all) B&B owners will make accommodation to meet you at your train or bus station, and/or return you there when your stay has ended. They're very good about that, especially as you get farther north. It doesn't hurt to call ahead and ask.
Trains will take you from Glasgow and Edinburgh to places like Dundee, Perth, Aberdeen, Elgin, Inverness, Fort William, Mallaig, Oban, Balloch (for Loch Lomond), Kyle of Lochalsh, Plockton, Strathcarron, Wick, Golspie, Thurso, and many places in between. Using a combination of trains, long distance and local buses, ferries, and taxis, you can reach just about anywhere you'd like to go. You mention that you've been to Scotland before, so there will be places that you want to revisit, and places that you want to see for the first time. You need to make a list, then connect everything using train, bus, and ferry schedules. If you want to get there, you're bloody well going to get there!
Getting back to weather - you need to travel light and carry a lined waterproof poncho, large enough to cover you and your luggage. It may never rain while you're in Scotland, but best to be prepared.
Have yourself a wonderful time on your return to Scotland, and best wishes for a Happy Hogmanay!