The end of March will be difficult especially at short notice, because it is the high season for Spring Break/Easter. Not only is it an expensive time of year, but a lot of places have been booked up well in advance and so you may have trouble finding availability.
I totally understand your GF's reservations about Cozumel. It's a wonderful dive destination and some divers (like my husband) take to drift diving easily and immediately love it while others (like me!) have a hard time learning to adjust to the current and maintain buoyancy and control. I finally got the hang of it and we have done many drift-diving trips including liveaboards, but it still isn't my favorite type of diving. I am always surprised when someone recommends Cozumel as the perfect place for a new diver, because it wasn't perfect for me when I was starting out - but everybody is different.
Florida offers a lot of what you are looking for, but the water is cold at that time of year IMO, and the same goes for the Bahamas. We went to Nassau in March once and I was freezing all the time while diving, never again! The further south you go the warmer the water, so Curacao may be a good choice. There are more topside activities on Curacao than Bonaire and you can do both boat and shore diving.
St. Croix might be a good option, there is a nice balance of tourist activities and boat diving and the Fredricksted Pier is a fabulous shore dive; I could dive the pier many times over and never see it all.
Grand Cayman offers lots of topside activities, and both boat and shore diving - but it may be a bit too expensive for your budget at that time of year, and it could also be difficult to find availability.
Shore diving is fun and it is a great way to save money, and it also allows you to adjust your diving schedule to accommodate the needs of travel companions, but some destinations (including the Caymans) do not allow solo diving so your shore diving opportunities may be limited - but since you are a new diver - maybe you wouldn't be interested in diving alone anyway? If you stay at a dive resort that offers onsite shore diving, it might be easier to buddy up with others staying at the same place.
Some places to consider on Grand Cayman include Cobalt Coast, it's all-inclusive so you will know what you are paying upfront and they have an onsite dive op and a house reef for shore diving. There's a lot of great places to eat on GC, but an all-inclusive might be a good way to control costs. If you took their cheaper package that only includes breakfast and dinner, you and your GF could spend some time in the afternoon exploring and sampling other food venues. Cobalt Coast is not far from the Seven Mile Beach and George Town but it is remote and it would be best to rent a car to explore the island. The CC shore diving can get winded out in the winter, but I think that late March may be okay - but you should investigate that.
Sunset House has breakfast included and both boat and shore diving onsite, and it's not far from George Town and there are 2 restaurants onsite. You could get by without a car but you'd probably need one for a few days to explore the island or visit the 7MB area.
The Grand Caymanian Holiday Inn has Divetech as the onsite dive op. They do not have a house reef for shore diving, but they will transport you to their Lighthouse Point property to shore dive or board the boats. The HI is not too far from 7MB and GT, but you would do best to rent a car.
There are lots of dive ops that service divers on GC and many will pick you up if you are staying on 7MB, and you can find inexpensive and convenient shore diving available at several locations on GC, but you will need a car and a dive buddy. Car rentals are usually pretty reasonable on GC but you'd be smart to reserve one in advance since you will be visiting during the high season.
It's cheaper if you stay in less developed areas away from 7MB and GT, but then you will need a car and you must be willing to travel to both the dive boats and many restaurants and entertainments. If you stay on the East End at Compass Point, Morritts, or Wyndham Reef, you can find good diving but you will be 45 minutes to an hour's drive from many restaurants and entertainments.
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@drrich2 says, there are places that might work for you, but maybe none of them will be absolutely perfect so you need to figure out what you like most, what you can afford, and where you can find availability at short notice, good luck!