Basically, I need to know if someone in late-19th century Scotland be able to readily identify bamboo. This is a weird niche question, but when you're writing a sci-fi time travel novel you're gonna get some of those I guess! :)
The earliest well-documented bamboo in Britain is Kew Gardens acquiring Phyllostachys nigra, black bamboo, imported from Japan, in 1826 (Kew Gardens says 1826, but many sources say 1827.) It is likely that Indian bamboos were grown earlier as hot-house plants, but Kew's black bamboo was the first (known) bamboo in Britain that would grow outdoors. Bamboo became more common in Britain (and continental Europe) during the 19th century, and a late 19th century Scot might well have seen bamboo first-hand if they had travelled in England.
There were various descriptions of bamboo, in writings about India, SE Asia, and China which could give enough information for a plant to be identified as bamboo. A major Western scientific publication on bamboo was Munro (1868). If your character was inclined to reading scientific literature, Munro's paper would be an excellent source, and might even enable identification of species. There was a popular book on bamboo (Freeman-Mitford, 1896) which sold well and popularised bamboo growing (Lucas, 2015), but this was at the end of the century, and perhaps too late for your character.
Beyond seeing living bamboo and reading about bamboo, bamboo was imported. For example, from 1836 to 1885, the British Army used bamboo hafts for its lances, Brighton Pavillion (the seaside resort of the Prince Regent/George IV) features bamboo, and included bamboo furniture (and rattan furniture, and imitation-bamboo furniture), and bamboo walking sticks/canes were popular. Bamboo was very fashionable in the early 19th century (even if much of the implementation of that fashion was faux bamboo). If your character has seen bamboo in such uses, it could be quite easy to identify living bamboo (but there might be confusion with other types of cane or rattan, in the absence of any description of how bamboo grows).
References:
Freeman-Mitford, Algernon Bertram Baron (1896), The Bamboo Garden, Macmillan. https://archive.org/details/bamboogarden00unkngoog/
Lucas, Susanne (2015), Bamboo, Reaktion.
Munro, William (1868), "A monograph of the Bambusaceae, including descriptions of all the species", Transactions of the Linnean Society 26, 1-157. https://doi.org/10.1111/j.1096-3642.1968.tb00502.x https://archive.org/details/monographofbambu00munr/