Reddit mentions of Panache Swim Women's Plus Size Panache Anna Tankini, Black, 28HH UK

I'm going back to the online retailer thing. You say you are in the states for a few weeks -- this seems like it could be plenty of time if you have somewhere to ship something. I'm thinking Amazon (which sells directly or is shipped by herroom.com or breakoutbras.com, both US retailers who ship quickly) or Breakoutbras.com directly, which offers 1-3 day shipping for $5.50. If you order now with expedited shipping, it'll ship tomorrow and arrive by the beginning of next week at the latest. I understand the qualms about online ordering, but desperate times, ya know? Ordering from US based places will drastically reduce shipping time, and you can also consider the possibility of reselling on /r/braswap, bratabase, or the facebook group for bra swapping as an alternative to return shipping if you find something affordable.

Also, forget about getting bottoms now or getting the matching ones all together. You can get bottoms anywhere, or if you really want the matching ones, you can get them on ebay when you get home (since you don't actually need the bikini itself for a few months). If you get any sort of top with black, plain black bottoms will work fine. This won't reduce the cost tremendously, but I am seeing 28HH-28J tops on Amazon for $45ish USD like this one or this one. If you are looking for a bikini top and not tankini, I see this or this for $60 USD. Going up a sister size gives a lot of options, and some of the bikinis are either tie-backs anyway and some bikinis can be rather firm (I have a 30FF in freya that is fine on my 26" ribcage). If you find anything fulfilled by amazon and know someone with an amazon prime account (even if they live no where near where you need it shipped), you can get free 2 day shipping.

If you want something basic, I really recommend freya pier. I have it in apple green, and it's very comfortable and lovely. I am clearly not familiar with your general bra needs like breast shape, but it's pretty narrow with a good amount of projection, and the ruffles are cute but not too in-your-face with all the boob. I wear a 30 band in it and it's fine for me, so a 30H may work for you. You also could very easily just make it into a tie back if necessary. The version I linked is the sweetheart neckline with two straps rather than a halter strap. This should be good as to not put strain on your neck, too!

Unfortunately, I have no recommendation for actual stores for you. I really hope someone does! It's rather tricky when you're past the GG+ barrier, I think, because even specialty stores don't always stock your size. I hope you find something you like, though!

Edit: Also, you may want to check out an old navy if you have the chance. They don't have bra sized swimwear, but I have seen a few posts here with ladies in your relative size range (small bands and GG+ cups) who have had success with their tie back underwire XL size swim tops. It is definitely an iffy thing, but you have the opportunity to try it on first. I think this option will totally depend on your shape and the width of the wires (and availability of the swimsuit in question!).