If you want to see more of Nepal, visit any of the tour offices or ask your hotel manager to buy a bus ticket onward. Nearly everyone supplies these so shop around and sometimes you can save a maybe 50-100 rupees on your ticket. The tickets will most likely be for the local bus and not the standard tourist bus like you may have come in.
If you want to go to India from Chitwan, you can buy a bus ticket the same way to the border tell them you want to go to Sonauli. Sonauli is the border town and is about 4 hours from Chitwan. When you arrive, you should be let off at the last stop after Lumbini, which is only a few minutes apart. Your bus will be swamped with touts wanting to take you the 2km to the border in their bicycle rickshaws. It should only cost NPR30-50 so bargain accordingly and remember to be clear that you are both talking about Nepalise rupees and not Indian rupees!. Note that some drivers will take you to a money change office just in front of the Nepal immigration office and then demand extra payment for the unscheduled read: comissioned stop. Just pay the formerly agreed upon amount and walk away. The immigration office is on the left side of the road. After getting your exit stamp don't let them try to charge you a fake exit fee, walk through the large "Welcome to India" arch and proceed straight ahead past the first grouping of police guards on the left and on to a small "office" that is a long table with 3-4 men sitting with entrance forms. The sign is small and so a bit difficult to see and is also on the left side of the road. After filling out your entry form and getting stamped you can either get a taxi to take you onward to your intended city or you can walk approx another 200 meters straight ahead to the bus lot on right side of road and ask around for your intended destination.
