Given the nature of balloon flights, it is not generally a good idea to take a standard bag filled with a large number of separate items of photographic equipment. Space in a balloon basket is likely to be limited, and time passes quickly. It is important to be ready to photograph subjects as the balloon passes close to them, so avoid wasting time with lens changes and adjusting accessories etc. A good solution may be to carry two camera bodies equipped with different lenses, much as a wedding photographer might. Both cameras can be supported on a neck-strap and consequently be ready for use at any time. Some photographers find that a spare camera hanging at near waist level gets in the way when leaning on the edge of a balloon basket, but this may be avoided by wearing the camera to the side of the body, perhaps with an arm through the neck-strap. Another possible solution is to use a waist-level holster style camera case.
As for all aerial photography is certainly important to attach cameras, and all other items of equipment, to your body or to the balloon basket. It is not only annoying and expensive to drop items of equipment from several hundred feet above the ground, but also very dangerous. The balloon's path may lead directly above people and property. Lens hoods should be attached to lenses, and lens caps are probably best left on the ground. Hot-air balloons eat lens caps! Spare batteries and memory cards should be kept in a zipped pocket. Other items that may prove useful include a lens cloth and a polarizing filter (preferably attached to a lens).
Hot-air balloon envelopes are very large, so a wid-angle lens is essential for many shots. Shots of the inflation of the balloon, the passengers in the basket with suitable backgrounds, the flaring of the burners all require a 17 - 35mm wide-angle zoom lens or something similar. A fish-eye lens might also be useful. Other shots, such as those taken from the balloon at altitude, may be better achieved using a zoom lens in the range 80 - 200mm. Shots of very distant subjected are likely to be hazy, lacking in contrast and perhaps less than critically sharp.
In summary, two camera bodies, one equipped with a wide-angle zoom and a lens hood and the other with a medium telephoto zoom, a polarizing filter and a lens hood, might be a good starting point. Both cameras should be attached to the photographer and spare batteries and memory cards should be readily available.
A final worthwhile addition to list of possible equipment is a GPS receiver. This can be used to store details of the flightpath and hence geo-reference images.