Whilst I don't think that this is either Tulipa tarda or Tulipa turkistanica (the petals seem to be too rounded), it is a closely related species. As the flowers start to go over I would begin to start feeding a half strength tomato feed every week until the leaves have died off. Then I would cease watering and allow the compost to almost dry out before repotting the bulbs in summer. This tulip is possibly Ok in the garden but is very nice in a pot.
{[ In past years I have treated similar potted bulbs by feeding every two weeks once flowering has finished. For the past couple of years I have been aware that flower power is diminishing so this year I am intending to feed every week once the leaves are established, even if they are still in flower]}.

I am not so sure of the identity. As you say it is in the same group as T. tarda (the Biflores section), but I will have to wait and see. Wondered if it was like some of the other Tulip species and need a very hot Summer baking? Do not usually grow Tulips in pots, I prefer them out on the rock gardens, but this one is only 4 inches tall and I reckon it would get lost.

Hi Owdboggy...I have a lovely tulip that looks like yours...its called Tulipa 'concerto' a fosteriana cultivar, .but a bit taller than 4"...about 20cm....:>)

Got the magnifying glass out and had a really good look at the flowers now they are fully open. It follows all the diagnostics for T. orthyrioides except the flowering time which is given as June. Maybe it is early having been kept n the greenhouse. The flower shape is very different to any of the fosteriana types.

I am having difficulty in finding pictures of Tulipa orithyrioides but the descriptions and location do match. Remember that the June flowering is in the wild where it grows at 3,000m (Tulips, Richard Wilford) so March in the UK would not be unreasonable.
From this location I would not dry and bake it during its summer dormancy. I would keep it 'just moist'.
Did you get the tulip commercially, Owdboggy, if so, from where?

Got it at the Loughborough AGS SHow, but for the life of me I cannot remember who was selling it. They did have a lot of rare tulip bulbs for sale though. Unusually I did not write on the label where I got it from either. Can tell you they were rather more expensive than I usually like to pay! :)

Yes, I would imagine that the sandwiches were cheaper than those tulips! It is a very nice tulip and if you have the species name correct, though, it was worth paying for.
Until you can bulk it up I would be inclined to keep it in a pot. When you have more you can try them in the garden.
Good luck with it.