Grafted Cherry Tree
There may be several reasons for few blooms. You did not mention if the cherry tree is a sweet or tart cherry. Sweet Cherry trees are self-unfruitful and require pollen from another variety within 100 feet to produce a good crop. If this is the case, you may need another variety that blooms at the same time. Tart cherries are self-fruitful.
Poor pollination - bee activity is low during cool wet weather.
Maturity - you did not mention the age of the tree. Sweet cherries begin bearing fruit in 4-7 years. Tart cherries 3-5.
Spraying insecticides during bloom and overuse of nitrogen fertilizers prior to bloom period. Also, severe pruning and stressful conditions such as drought, low temperatures, and wind will reduce the number of blooms.
See our publication and our website for more information on stone fruits