Would I need to buy a dedicated bolt for both of the barrels
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You [i]should[/i] have a bolt for each barrel. (It will [i]probably[/i] be OK to use the same bolt, but be sure to check headspace each time you install it to make sure it's safe.) Using the same carrier is OK.
ordering a 20" barrel and swapping it out as needed
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Swapping barrels is not something I'd want to do on a regular basis. If I understand correctly, you have a free 24" SS barrel, and a free A2 upper. Given those two parts, I'd order a kit with a flat-top upper and then put the 24" SS barrel on the flat-top and the 20" barrel (or whatever) from the kit on the A2 upper.