You'll have to wait a while because each bush blooms at a certain time of year and for a limited number of days. The hibiscus plants all bloom from June 28 to July 5th, and from July 6 to September 15th, according to this wiki. You should start to see them bloom in a few more days.
When Leif is visiting your island, you can buy new bush starts from Leif's Flower Shop outside of Resident Services in Animal Crossing: New Horizons. Unfortunately, this happens at random, and you have no power over how often or when Leif appears. The shrubs take three days to completely develop after being purchased from Leif and planted.
The reasons for no bushes blooming in ACNH?
On the beach, shrubs don't grow.
Shrubs may be planted on the beach, but they will not flourish. On the other hand, you can't transplant fully grown shrubs onto the sand.
Seasonal Blooming of Shrubs
It's worth noting that each shrub blooms only during a particular season. It is not blooming season if your fully grown shrub is not blooming. Cross-pollination of shrubs to produce new hybrid varieties does not appear to be feasible, as it is with normal flowers!