This paper presents a pair of formal concept search procedures to find associative connection of concepts via bridge concepts. A bridge is a generalization of a sub-concept of an initial concept. The initial concept is then shifted to other target concepts which are conditionally similar to the initial one within the extent of bridge. A procedure for mining target concepts under the conditional similarity with respect to the bridge is presented based on an object-feature incident relation. Such a bridge concept is constructed in the concept lattice of person-feature incident relation. The latter incident relation is defined by aggregating the former document-feature relation to have more condensed relation, while keeping the variation of possible candidate bridges. Some heuristic rule, named Mediator Heuristics, is furthermore introduced to reflect user's interests and intention. The pair of these two procedures provides an efficient method for shifting initial concepts to target ones via some bridges. We show their usefulness by applying them to Twitter data.