The mountain road between Kathmandu and Pokhara is called “highway”, although it would not qualify not even as a secondary road as per other standards – average speed 30 kms/h.
To reach Bandipur from either Kathmandu or Pokhara, your first stop is Dumre, a town halfway in between.
From Chitwan, take any bus heading for Kathmandu and get off at Mugling. The 1 hour distance between Mugling and Dumre is served by many vehicles, form vbuses to minivans and even shared taxis.
From Dumre, jeeps to Bandipur leave from the main road. Just ask the locals, they will show you where. The 7km road up the mountain is done in 20 minutes, and a fare would be 20 rupees. From Bandipur, jeeps to Dumre leave from the main road or from the town square.
In reality, the situation on the “20 rupees fare” is a little bit different – having timing constraints to catch buses for other destinations from Dumre, you won’t like waiting too long for the jeep to get full (10-15 passengers), so you’ll prefer to hire the whole thing. The driver will say “400 rupees and we leave now”. You have 2 choices (I’ve tried both): accept you pay the 400 rupees, and offer a free ride to the other people who will start jumping around from virtually everywhere (insist that the driver does not ask the locals to pay anything), or bargain down to 300 rupees and let the locals pay 20 rupees each.