I agree that this is Edinburgh 1888 and I would say the maker is JB.
Edinburgh Incorporation of Goldsmiths list a JB mark for John Finlayson Bain, but do not illustrate it so I cannot be sure that your spoon is actually by Bain. However they note that Bain is mentioned in their records between 1888 (earliest) and 1906 (latest), so circumstantial evidence certainly points to Bain.
There is an illustration of a virtually identical JB mark by James Berry of Aberdeen (mentioned 1857 to 1890), but I would have expected anything by him also to have ABD or ABDn on it. There is also a similar JB for J Brown (earliest mention 1890).