Although eBay.com's Mud Truck category mostly shows mud trucking accessories, its 4x4 Lifted Truck category has vehicles appropriate for mud bogging. Some of the listed vehicles have tires appropriate for mudding.
Organizations have different definitions for what makes a truck a mud truck, but most mud trucks have lifted suspensions, and many drivers use tractor tires or tires with similar designs. Many of the lifted trucks on eBay.com have standard road tires, but a tire replacement can make them appropriate for mudding. Since much of the challenge of mudding deals with avoiding getting stuck, almost all mud trucks are four-wheel-drive vehicles. It's important to note that mud bogging leagues have different rules, so potential participants might want to review them before purchase.