Actually there is an airport in Bonito, although there are only 2 flights in and out per week - on Wednesdays and Sundays with Azul, to and from São Paulo. Obviously you can get connections from other cities.
For the south Pantanal there are actually several ´gateways´, the two most popular are currently Campo Grande and Bonito, although several years ago Corumba was considered the main gateway to the south Pantanal.
True Pantanal technically starts shortly after you pass the town of Miranda, which is about 2 hours from Bonito and 3 hours from Campo Grande. In the south Pantanal most tours take place along the Estrada Parque, which is a dirt road which splits off from the main road between Campo Grande and Corumba at a point called Buraco das Piranhas, about an hour north-west of Miranda.
The north Pantanal really only has one gateway, which is Cuiaba, although the Transpantaneira road starts from Pocone, an hour or two away.
If you are on a budget, it´s best to visit the south Pantanal.
