The testing supplies can usually be found at a local parts store.... NAPA, Checker, Kragen.
As for the coolant exiting the system when you're trying to burp it, I know, mine does that as well. After replacing my HG and all of my coolant lines I've never had to "burp" the system as everyone recommends, any air introduced into my system works it's way out just fine.... but that could be due to the large top tank of my after market radiator.
As for the almost new items, I've seen brand new, never used radiator caps fail pressure testing. Call around, some auto parts stores and service shops have tools to test radiator caps and thermostats (under pressure, not just tossing it in a pot of hot water
). Usually it only costs a couple dollars if they don't do it for free.
The coolant is bubbling out either because air is exiting the overflow tube into the reservoir which should be about half full. Like blowing air through a straw into a drink. The air is coming from somewhere, and if it's constant it's most likely combustion gasses.