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You can first compute the cohomology algebra in a range of dimensions:

HB = B.cohomology_algebra(10)

Then you can form an exterior algebra using either a basis for HB in a particular dimension or all of its algebra generators:

ExteriorAlgebra(QQ, HB.basis(1))

or

ExteriorAlgebra(QQ, HB.gens())

One potential difficulty is that the generators have been renamed when computing cohomology, so it may be hard to tell where they came from in B. You can try to recover that information using B.cohomology_generators(10), which lists the generators in each degree. You can then match them up to HB.gens().