A bushing (30, 31) in a hole (26) through a ceramic matrix composite structure (20) with a flange (34, 38) on each end of the bushing (30, 31) extending beyond and around the hole and pressing against opposed surfaces (22,24) of the CMC structure (20) with a preload that resists buckling of the composite structure fibers and resists internal CMC fiber separation. A connecting element (40), such as a bolt or pin, passes through the bushing (30, 31) for engagement with a supporting element (50). The bushing (31) may be formed in place as a single piece of ceramic, and cured along with the CMC structure (20), or it may be formed as two ceramic or metal parts (32, 36) that are joined together and preloaded by threads (33). The connecting element (40) may be a pin, or it may be a bolt with a shaft threaded into one part (32) of the bushing and a head (42) that pushes the second flange (38) toward the first flange (34).