Data structure for a static set of sets
Generically, these are sometimes called subset/containment dictionaries. The fact that you had partial matching in your question (but deleted it) is actually not a coincidence, because subset/containment queries and partial matching are equivalent problems for sets.

You probably want to use an UBTree (unlimited branching tree) for this; it's basically a modified trie. See Hoffmann and Koehler (1998) for more details.

You could also have a look at the more recent set-trie data structure proposed by Savnik (2013) for the same purpose. (If you miss the color in the graphs in that preprint paper and don't have access to the official Springer publication [in which the colors aren't missing], there's precursor to that paper which has almost the same graphs/info and no missing colors.)

Both papers (Hoffmann &amp; Koehler, and respectively Savnik) have experimental results, so you can have some idea what they can handle in practice. Both seem to handle data sets with a cardinality of U around 1M.

If you somehow have TCAM hardware (or the money for it), there's a way to leverage that for subset/superset queries. You can actually do both subset/superset queries in parallel assuming you have enough TCAM words (2x |U|). 
Since TCAM words can be configured to be 144-bit wide, you and you have only 95 bits/letters to test, you wouldn't even need to bother with Bloom/hashing, you'd have an exact test using TCAM; this is trivial enough I'll even say here how: every {0, 1} bit-vector corresponding to every set in your U is simply turned into a {0, *} vector for subset queries and to a {1, *} vector for superset queries.

A more general problem tackled in ETI (no free copy, sorry) is finding a set with given similarity measure. For example, the similarity measure can be $J(Q,S)=\frac{|Q\cap S|}{{|Q\cup S|}}$ and the query for a given $Q$ can be to find all $S$ (in the database) with $J(Q,S)\geq 0.3$. Both the constant and the similarity measure are user-definable as a predicate in ETI. (The $J$ given as example here is called the Jaccard index.)