Yes, as a matter of fact, you can use the GI Bill while you are on active duty. In many cases, however, you get less benefit out of it this way.
If you are using the Montgomery GI Bill, you can apply to use the benefits while on active duty. However, if you are on active duty, you receive either the normal monthly MGIB payment, or the monthly cost of your courses, whichever is less. If you are also using Tuition Assistance (TA) from your service, you can only use the GI Bill to pay the portion of tuition that is not covered by TA. Since most of the services’ TA programs are not paying 100% tuition, this should only come up if your courses go over the maximum amount of TA.
You can use the new Post 9/11 GI Bill while on active duty as well, in a similar manner. Not, however, that if you are on active duty, you do not receive the housing stipend or book allowance.