Bare root plants are always best planted in autumn, or they have trouble getting enough water while they settle in, as you've discovered. Hopefully, after another 3 weeks it may have put out some decent water seeking roots - in the meantime, you haven't said how much water you're giving it, but the best thing to do is to give it around 6 litres every time, which will hopefully extend the period between waterings. You want the soil beneath the plant to be wet so that the roots go down - if you're only watering a bit every day, this just wets the surface, and the roots will come up and wait for you to come along and give them some water.

If you can't get anyone to come and water in that 3 weeks, there's not much you can do other than hope the weather here isn't too hot or too dry. I'd certainly suggest you give it a thorough soaking for at least 3 days before you go, then mulch over the top, 3 inches deep, and a foot wide all round with something or other (bark chips, composted manure, garden compost, whatever). This will help keep the soil moist. Don't, though, pile the mulch against the main trunk, leave that clear about half inch all round.I wouldn't worry about the flowering now - it was obviously prepared to flower, but didn't get planted in time for winter.

We bought an automatic watering system from hoselock. It is easy to set up and it will water your plants up to 4 times a day between 5 to 15 minutes

I had a plastic gadget which screwed onto an empty plastic drinks bottle which you sank into the ground beside the plant. It drip watered and worked quite well. I think it came from the £1 shop or the likes. I came with more than one gadget so you could use a couple.

Nijiiann - I can't have automatic watering system as I don't have an outside tap.
Cammomile - I will look out for the plastic thing but I tried this last year for my indoor plants and either the nozzle got bunged up or all the water gushed out in one go - but will try again, don't think even a 2 litre bottle dripping would be enough though.
Bamboo - I have been giving it a 2 gallon can of water every other day, it is mulched but only with gravel

Gravel's better than nothing, but organic mulches tend to hold more water... and I'm glad to hear you're watering it well!

Would surrounding it with a plastic sheet help or do more harm than good?

I don't know if plastic would help, but it would be ripped off by the foxes the first night - as was the black fabric I originally put under slate and gravel, they just dug it up and ripped it to pieces. [the squirrels had a go too]

Time to invest in an outdoor tap!

Can't have an outside tap - I live in a first floor flat and my garden is detached.
I have tried various different ways around this but so far there doesn't seem to be a solution.

Oh I can understand now. What a shame you can't ask a neighbour.

Yes it is a shame, I live in a very small cul-de-sac [banjo]
and my neighbours are all even older than me with varying levels of disability.

Perhaps in three weeks it will have grown enough new roots to survive...

Hope so