When my first choice hired me and gave me a class date, I sent emails to all the other regional airlines I had interviewed or pending interviews with; expressing gratitude for consideration, but had made my decision to accept a conditional offer elsewhere. That simple.
These professional recruiting departments aren't like some of the shady 135 operators out there that get butthurt when you don't jump on the offer, or when you leave, etc. They're not going to see personal at all, just two parties failing to come to a mutually agreeable exchange of services for money. Do pilots take it personally when an airline sends them a TBNT?