What is a polite way to tell a Scottish person that I am struggling to understand his/her accent?

This is a personal experience answer. I am Dutch, so maybe a bit more blunt than you, but my solution works well.

I had that same problem last summer. I had arrived in Edinburgh one day, went to visit Glasgow the next and the first person talking to me was hard to understand.

I explained to the woman that English is not my first language and I had not adjusted to the accent yet. She understood and talked a bit more slowly and that was enough for me.

Mostly when you take the blame on yourself, 'my understanding of English is not very good' people understand that you do not want to blame them. And people in the different parts of the UK are used to tourist not understanding them. But they also know that they do not speak much (or anything) besides English, so they do appreciate your speaking their language, however limited.

Funny side note, in the past I have translated for a Scot in France. We were a group of volunteers (with English as only common language) and the guy had to read a list of jobs and ask for the number of people needed. I had been there before and more or less knew the list, at least the regular jobs. And the guy the year before had had a mild Scottish accent, so I was used to the sound.
Many of the other volunteers had never heard anybody with a strong Scottish accent and did not know what to expect. Specially the Americans in the group did often mention not being able to understand it at all. Fun and it did improve my English, certainly the understanding part. I was only 19 or 20 at the time and not yet fluent in English, so I was rather proud it worked.

From personal experience I can say that asking politely to repeat what they just said helps the most. "Beg your pardon?", or "I'm sorry, what?" or "I'm terribly sorry, but I didn't understand you" all worked very well for me. I never had the feeling that I offended the speaker.