No public transport connects Musanze to the the Rwanda Volcanoes Park headquarters at Kinigi, 13 km from town, nor does it from Kinigi to any of the car parks from where one enters the forest to start tracking.
Individual travelers may be able to beg fits with other tourists, but for larger transport-less groups the only option is to hire a vehicle and driver for the morning.
ORTPN in Musanze can advise on this and Highland Gorilla Tours & Travel can arrange vehicle hire. In the rainy season you will probably need a 4 x 4; in the dry seasonal ordinary taxi voiture should be adequate and will cost far less.
The going rate for a 4×4 from /to Musanze is around US$60 for the round trip; tour operators in Kigali can organize it as a day trip from Kigali for around US$150, or less if several of you share a vehicle.
If you spend the night beforehand at the Mountain Gorillas’ Nest, the Kinigi Guest House or the ORTPN Campsite, all quite close to the Kionigi park office, you stand a reasonable chance of hitching a lift up there from the main road; but you will still need transport in the morning to reach the start of the trek. Whatever method you choose, make sure that it is reliable – if you don’t turn up at the appointed time you risk invalidating your permit and having to pay again.