Instead of everyone here being redundant you should probably thoroughly read every thread on the first three pages of this forum for most of what you might want/need to know about non-bloomers.

Also, I'd caution anyone to not buy or grow anything until they've read care instructions and/or researched first.

For starters, it would help you to know your USDA hardiness zone (Google it and check your location) as well as what kind of hydrangeas you have (there are many).

As a general rule, late September or April are good enough times to move any hydrangea.

Sounds like these non bloomers are probably H. macrophyllas that only bloom on flower buds that develop from July to August and that bloom in the Spring They may not be winter hardy to your zone and the buds get killed by winter When that happens, the growth returns from the base/crown.

To confirm, please say where are you, post pictures and let us know the variety you have.

It may not be wise to transplant water hungry shrubs in the summer. Perhaps wait until they go dormant in the Fall instead? However, this move is needed only if the shrub is in dense shade as they usually bloom in dappled sun and bright shade.

Other causes to consider: too much fertilizers (once in Spring is typically enough if you have no soil mineral deficiencies or sandy soil) or pruning at the wrong time (flower buds in non-rebloomer mophead hydrangeas develop in July-August so prune before the end of June).

If you add a photo of the plants as well as the zone and location, that will help answer many questions we have so that you can get your question answered.