"Bidirectional assimilation" is an unlikely name for that kind of case, which constitutes "gemination" or "geminate formation". "Bidirectional assimilation" is generally used for the assimilation of a property which both affects a segment on the left and a segment on the right. ATR and nasal harmonies are the canonical examples, where e.g. /wemao/ → [w̃ẽmãõ].
When the result of combining two distinct adjacent segments is a single long segment, we usually refer to the process as merger or fusion, possibly adding a form of the word "geminate" to indicate that the result is a geminate consonant (for instance, /hy/ → [ʃʃ]). In the specific example you give, no feature is contributed by /s/, and /tʃ/ doesn't become in any way "more like" the deleted /s/. You might encounter a case that could be called reciprocal assimilation, where in a sequence of segments /AB/, A takes some property from B and B takes some property from A, and the result is surface DE (not a geminate). The most common case of that kind involves progressive post-nasal voicing, and regressive place assimilation, whereby /mk/ → [ŋg]. However, this is not "a bidirectional assimilation", it is two assimilations, one regressive and the other progressive.