Unemployed Grad Student:
If you are truly on a budget Ambergris Caye will most likely break it. It is at least double the price for most everything, food, lodging, diving, drinking, etc. Instead consider taking the Ambergris money and upscaling your Caye Caulker lodging, you will still be lots of money ahead.
If you simply must see Ambergris there is speedboat (watertaxi) service between the islands several times per day. You could also perhaps get a dive shop to give you your surface interval at a restaurant there in between dives.
As for shore diving, forget it. The reef is only a 1/4-1/2 mile offshore but too far to swim. There is a shallow sandy area between the shore and the reef that has little to see but seagrass. Since the reef is so close the diveboats arrive in no time.
I have my favorite places to stay and diveshops to use. I'm sure everyone does.
Go have fun.