Quoting Jason Stajich's response on the BioPerl mailing list:
Bootstrap is not a fixed newick field - best thing is to set the internal ID to the bootstrap value, that is where it is read from when writing a newick tee.
replace $node->bootstrap( ... ) with $node->id( ... );
Or use NHX format which has separate fields for bootstrap and ID.
There is also a connivence function which will copy IDs to the bootstrap field on the whole tree, (move_id_to_boostrap defined Bio::Tree::TreeFunctionsI) but there is not a corresponding reverse function that would move bootstrap to id at the moment, though it would be trivial to add this patch if you think it is useful enough.
Or if there is a good way to apply Fst values as bootstrap values using a different mechanism than BioPerl, then I'll take that too (begrudgingly)