I first read this book as a child. I remember it as being moving, if on the sappy side. That's true, but the book also has flaws I didn't remember at all.
The language is stilted and overwrought. That's especially evident in the slow, slow start, which seems intent on describing Edinburgh in as much detail as possible. It keeps us from getting to the good part, which is obviously the dog, and it's not particularly interesting in itself. There's a tremendous amount of exposition, and that continues throughout.
There's also a heavy emphasis on a Scots accent. In the dialogue, that works quite well. But Atkinson often, and inconsistently, carries that through into the exposition, where it's a very awkward fit.
The actual story of Bobby is nowhere near as strong as I recall. It's obvious from the start that a great deal of it is invented, and yet the story is written as if it were reporting history. It's not too heavily anthropomorphic, but it's definitely sappy, and it's very, very slow.
I'm sorry and surprised to say that I think this is a book whose time has passed. While the base legend is nice, and I'm in favor of any story that encourages people to think hard about animals, this book really isn't that good a read, and I think there are now better options.