The only scheduled USA flight into BFS is the United Newark service. According to the Spokane airport wiki, United fly Spokane-Denver. Therefore to fly into BFS you could do Spokane-Denver-Newark-BFS.

The suggestions to fly into Dublin instead are sound ones. Not only will you have more options, but likely the flights will be cheaper (even allowing for the waiver of UK APD on the united BFS flight).

For example, You could fly Spokane-Atlanta-Dub on Delta. You could also fly Spokane-Chicago O'hare on United, and then Chicago-Dub on Aer Lingus.

There would be other options as well.