I bought a hibiscus start from the Island and planted it. It grew to full bush size days ago, but there are still no flowers. It's summer so I figured it would flower just like the island.
Are there conditions to making the bush flower?
You have to wait - each bush blooms at a different time of year, for a specific span of days. According to this wiki, the hibiscus plants all flower from June 28 to July 5th, and flower from July 6th to September 15th.
In just a few more days, you should start to see them flower.
For reference, this image shows the different stages of each bush: