I have Bushmaster and RRA bolts and carriers and have never had any problems.  I have one RRA upper with a Bushy carrier and RRA bolt.  It shouldn't matter, as long as everything is in spec.  Just because a part is Colt doesn't mean it's necessarily going to work though.

Checking headspace requires having headspace gauges.  Unless your gunsmith already has the gauges, knows how to use them and isn't going to charge a lot, I'd vote for buying the gauge.  It's not a bad thing to have.  You could get by with a field gauge only, but I like having the go and no-go gauges also.