Hello, Patricia. The answer depends on what type of hydrangea you purchased. I am hoping that, based on your zone 3b, that it is either a hydrangea paniculata or hydrangea arborescens. Under typical conditions, both of those hydrangeas produce flower buds in late Spring or early Summer and then they bloom in the Summer. So you may just have to wait a bit more to see bloomage. Also, some paniculatas bloom earlier or later than others so that too can make a difference but regardless of which paniculata you have, it should blooms in the summertime.

As soon as the shrub develops a good/larger root system, it will grow more and faster. But I generally do not worry as some shrubs can take 1-3 years to grow fast. It depends on such things as how big (or small) of a root system it had In the pot, etc. I would not expect much change in just one month.

In the meantime, you can maintain the soil as evenly moist as you can without no dry periods, followed by wet periods and back to dry periods. A new hydrangea shrub usually does well with 1 gallon of water (1.5 in the Summer) per watering; water when the soil feels almost dry or dry. You can also maintain mulch all year around, about 2-4" up to the drip line or thereabouts. If the plant had those round fertilizer pellets that nurseries add, there would be no need to fertilize it this year. You can also check your soil pH and acidify it if it is alkaline (amend with either greensand, aluminum sulfate, garden Sulfur, etc).