I'm assuming that currently you are using a While Loop or For Loop in order to acquire each of your records. Inside the loop, you configure the acquisition, read the data, and then save the data. Is this close?
You will be able to save quite a bit of time by storing the data in memory instead of writing to a disk. You can do this in LabVIEW by simply using a shift register or index your data as it comes out of your loop structure. You will want to make sure that your PC has enough RAM to store all of that data and still run your programs at the same time.
Once your acquistion is done, you can do any kind of post processing that you want and finally save to disk.
20 us is very fast and I'm doubtful that you'll be able to setup the 5102 in software quick
enough, but I haven't personally tried. If the 20 us is a hard and fast requirement, you might want to consider something like the 5122 which can do a multi-record acquisition, has a fast trigger rearm time, and can have up to 256MB per channel of onboard memory .
Good luck,
Jack