There really isn't anything intended for that purpose. It is more a case of the plant being established long enough for the current season's growth to be robust enough to generate flowers. In areas where the current season's growth accounts for the majority of the flowering (i.e., colder zones), that seems to be somewhere in the 3-5 year range according to reports here in the past.

So-called "bloom booster" fertilizers are really intended for annuals and very seasonal crops and have little to no impact on any woody plants.

For newly purchsed shrubs from your local nurseries, you can apply 1/2 cup (or so) of cottonseed meal, composted manure, organic compost or even a slow release general purpose chemical fertilizer with a NPK Ratio of around 10-10-10 (per label directions - you can also use half as much too). Will it help with reblooming? It will not hurt but too many variables come into play there but that is another story. I apply whatever I happen to have each year in Spring (usually one of the above). You can also not fertilize. Hydrangeas do not need large amounts of fertilizers like roses do. I have forgotten to fertilize in some years and they fed off the decomposing mulch (maintain 2-4" year around) and minerals already in the soil. I have drip irrigation where the hydrangeas are planted.