All it says is Orchid "Bordou" so I would imagine that Bordou is just a name for this orchid and tells you nothing about it!

Might I suggest that buying an orchid in a poly. bag from a market in Madera is possibly not the best way to go... especially if you want to be able to i.d. I am assuming it isn't in flower right now, when it is take a photo and put up and, hopefully someone will recognise.

Bordou would probably be the same as Bordeaux; although the translation of bordou is embroidery. I am not surprised you were able to buy an orchid in a plastic bag since orchid culture is a big deal in Madeira. There are a lot of specialist nurseries on the island, and one sells on E-Bay.co.uk (Madeira Exotics is the shop name). São Miguel has pineapples, Terceira has proteas - and you can buy rooted cuttings in the market.

Incidentally are you allowed to import plant material from Madeira? I think import regs are being tightened up in view of all the diseases coming in? They are watching trees carefully, don't know about small plants.

As far as I know, there are no restrictions inside the EU. I receive (in Portugal) plants from the UK, Germany, Belgium, and Ireland. Because of the olive tree problems in Italy, it resulted in new restrictions on importing:
http://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX:32015D0789&from=DE

There are all sorts of new rules and regulations regarding live plant material imports Stera. even within some parts of the EU, I'd have been very wary of doing so.

Not sure but I think Madeira is considered part of the EU! It is part of Portugal.

Excellent info on growing your orchid on this website http://mag.plantes-et-jardins.com/conseils-de-jardinage/fiches-conseils/orchidees-phalaenopsis-rempotage-entretien. It is in French but it will translate in to English for you.

If you can show us a picture of the plant, even without blooms, we could probably tell you what general group of orchids it is in, which would tell a great deal about culture.