House Tyrell wasn't much of an ally, it seems. They couldn't even keep the loyalty of the Tarleys.
So Dany has the remaining Unsullied, who are alone in a part of the continent where they're vulnerable, and the Dothraki. Did they bring their horses across the Narrow Sea?
Even if they did, they are not of much use on that island, unless they're encamped somewhere on the continent.
Seems like Dragonstone isn't necessarily the best strategic place to be, other than the dragon glass, which Dany didn't know about.
If not for the dragons, it would be easy to do a naval blockade. In fact, where do they get food from? It would be inefficient to bring it up that narrow bridge and steps. The real life island is very small and not really meant for a castle.