An example of untrasportable sentence, when there is only one principal base set X, may be the following one:
All elements of the set X are finite sets,
Because, by definition, the truth value of a transportable sentence must be preserved under all bijections from the set X. Obviously, there exists a bijection from X to a set Y, where not all elements of Y are finite sets.
A simpler example is "the set X contains the empty set".
There is a paper "Sentences of type theory: the only sentences preserved under isomorphisms" by Victoria Marshall and Rolando Chuaqui - see The Journal of symbolic Logic, vol 56, #3, Sep 1991.