A method for mounting beads on a tire carcass which is being laid up on tire building drum, particularly applicable to cases wherein the drum has a free end and an opposite end which is supported by a drum support (or comparable impediment to installing a bead from the opposite end of the drum). The method comprises disposing a first of two beads on the drum in an area which is between a carcass layup area and the drum support. The bead is moved into this position from the free end of the drum, and this is done before the process of laying up the carcass has resulted in there being an impediment to installing the bead from the free end of the drum, such as bumps resulting from tire insert components. This may be prior to any carcass components have been laid up, or after an inner liner has been laid up, or after an inner liner and inserts and a ply have been laid up on a drum having pockets (recesses) to alleviate bump formation. With the bead “parked” on the drum, yet out of the way of laying up the carcass, the carcass may be laid up. After laying up the carcass the bead is moved into position on the carcass. Then, additional tire components may be laid up on the tire carcass and/additional steps performed in the formation of the carcass. The other bead is installed onto the carcass in a conventional manner. In this manner, both beads may be installed from a one free end of a drum. A bead loading system includes a rail, two carriers hanging from the rail, and a bead holder at the end of each carrier. In a flexible, automatic tire building system having a sequence of work stations, after a completed carcass is removed from a drum at a last one of the workstations, a first bead for a subsequent carcass can be placed onto the drum at the last workstation, before the drum is re-circulated to the first work station.