Bandipur is roughly half-way between Kathmandu and Pokhara, above the Prithvi Highway, and is a popular place to stop for a night or two to break the journey. Chitwan National Park is also roughly equidistant from Kathmandu and Pokhara, on the Terai plains bordering India.
Most visitors to Chitwan stay in or around Sauraha, in the east of the park, as there are many hotels and tour operators here. However, the quieter village of Barauli is another option, to the west of the park. There are a few nice places to stay here, including the high-end Tiger Tops Tharu Lodge. Most people will assume you're heading to Sauraha, so make sure you know where you're staying in Chitwan before booking transport.
Here's how to get from Bandipur to Chitwan.
By Private Transfer
Duration: 3+ hours
Many travelers book a private transfer to take them from Bandipur to Chitwan. Bandipur is a couple of miles up a steep hill from the town of Dumre, on the Prithvi Highway that connects Kathmandu and Pokhara. An advantage of private transfers is that they can pick you up directly from Bandipur, without you having to make your own way down to the highway first.
From Dumre on the highway, you'll first travel a little way east (in the direction of Kathmandu) and then turn south towards the Terai at Mugling. This stretch of road has been undergoing roadworks for several years, and while the worst of it is reported to be over, don't be surprised if you get stuck in a jam around Mugling.
Duration: 3+ hours
Less convenient than a private transfer, tourist buses are another option if you're on a tighter budget.
All buses traveling along the Prithvi Highway between Pokhara and Chitwan can stop in Dumre, on the highway, on request. Travelers can pre-book a tourist bus from an agent in Kathmandu or Pokhara, who will advise of the best time to stand on the highway and wait for your pick-up. A local cell phone number is a handy way of tracking the progress of your bus, so you don't wait for too long at the side of the road for a bus that's running late. If you don't have one of your own, helpful hotels will usually be able to track this for you by calling the company or driver.
From Bandipur, most accommodation can arrange for a private transfer down to Dumre so you can meet your bus. They may charge a little for this. Local buses also leave Bandipur periodically, from the end of the road at the entrance to the town.