One problem with companion plant groundcovers with bulbs is the companions will often need watering through summer when some if not most bulbs are dormant & regular watering would cause them to rot.
I've found ornamental strawberries can get by without TOO much summer watering, plus can bloom spring through autumn.
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poscharskyana, or Serbian bellflower, also thrives with spring moisture & summer droughtiness, & in my zone blooms for about six months right into the heart of autumn.
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lemon thyme is a good groundcover companion for the sorts of tulips that need it very dry in summer.
Ballotta nigra 'Variegata' is a loosely trailing groundcover; the root remains a clump but the branchings can cover a four by four foot area, & I have it planted with two-foot or taller tulips.
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other herbs do well in lots of sun without need of too much watering & remain short enough & not too densely rooted that they do well well over bulbs. Such as Tricolor marjorum:
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the ratgirl