Are u arriving via Fishguard? There's a good Tesco Express as you exit the port - you could pick up stuff for the evening with only 40 mins left in the car. And the kids could go to the playground opposite.
Book your golf buggy in advance as sometimes they get sold out.
The Tesco Extra in Haverfordwest has a click and collect service - that's 20/25 mins from Bluestone.
Many thanks to those who came back to me with information and advice rather than a pointless attempt at sarcasm, its much appreciated and good to know you enjoyed your stays.
Well be arriving at Bluestone at the end of a 9-hr car and ferry journey from Ireland as we are driving there to see my family beforehand, car will be packed to the gills with stuff so popping to shops not an option. While I am a bit of a default Internet-shop person (3 kids under 3 so find shopping hard work) that does not stretch to expecting a van to deliver to the door of a car-free site, just to the gate! Hopefully we can rent a buggy or something which should help. Thanks again 
We had an Internet shop delivered at home just before we left London and topped up with the shop there plus Sainsbury in Tenby. I'd be pissed off if Tesco vans were driving around a car free site, so I expect you'll be collecting from the Car Park and if you happen to be staying on the far side of the resort that won't be much fun.
We also took a couple of home cooked things (pasta sauce, a curry) that I'd frozen so we had quick food when we were in a rush.
We stayed at Bluestone a few weeks ago, and like OP says, it's a car free site apart from on check-in and check-out days. How are you planning on getting around the site? Are you aware it's pretty hilly and depending on where you're staying, you may have to lug all the shopping from the car park area at the top of the site? I guess if you've arranged a specific time to have the shopping delivered you could meet before the check-in area? We just did a big shop before we left and put frozen/ chilled stuff in cool boxes. There is a Morrisons not too far away in Haverfordwest that we called into after a day at the beach in Tenby too.
Hi, I am looking for advice from those who have recently been to Bluestone in Wales please has anyone experienced difficulties receiving a Tesco delivery at their cottage? We are going there in a couple of weeks with a extended family group, and when I phoned up to check if there was anything specific we needed to do when receiving an Internet shop e.g. let the folk at the entrance gates know, I was told that they dont support it, although obviously they cant stop vans from coming in as they now have their own (v. limited) food ordering facility. Am going to go ahead and order it anyway, but interested to know others experiences as I dont really relish the idea of some kind of standoff at the gates so would like to be prepared! Also, can anyone recommend a good butcher/farmshop/delis in the area, or a nice place for a dinner out preferably the rustic pub kind - to take advantage of grandparent babysitting? Many thanks in advance.