The drying time of a Henna tattoo is dependent upon the type of Henna used. Many new types of Henna have been introduced in markets which give color within a few minutes.
A typical Henna type takes around an hour to dry and give good color.
I prefer to keep henna longer than 1 hour because even if a henna tattoo has dried, it does not mean that it has given the best possible color.
I suggest keeping a Henna tattoo on your body parts where it is painted for around 2-3 hours.
TIP: Apply Henna tattoo at night or anytime before sleeping. When you will do so, Henna will get more time to remain on your body and hence give the best color possible.