I'm writing a web application. I deal with a lot of objects as users, events, orders, customers and so on. These objects act as business objects ( they handle the state of the application). So, many of them must be persistent ( MySQL DB). So i would like to use Hibernate as O/R mapping layer.
My question is : is it a good way to make persistent my business objects ?

yes ;-)

To be more specific, Hibernate is done for that.

So if i want to use DTO Objects, do i have to use my business objects to do so or do i have to create objects that will be similar to my BO.
In fact, if i use a set method on a BO which is persistent, for example, in a servlet, i have an error because no session in opened.

Normal approach is to use the business object (domain object) as your DTO. You just have to make sure when you dealing with the persistence layer you have an active transaction and session. There is lots of information on the wiki, FAQs, manuals and the forums. Take the time to do some research.

this thread might be of some help:

http://forum.hibernate.org/viewtopic.php?t=925766