JavaScript (ES 6, feedback welcome!)

function Driver(route) {
    this.id = Driver.drivers.length;
    this.route = route;
    this.stop = 0;
    this.numGossips = 1;
    this.gossips = {};
    this.gossips[this.id] = 1;
    this.getStopName = () => this.route[this.stop];
    this.drive = () => this.stop = (this.stop + 1) % this.route.length;
    this.heardItAll = () => this.numGossips === Driver.drivers.length;
    this.receiveGossip = gossip => !this.gossips[gossip] ? this.gossips[gossip] = ++this.numGossips : null;
}
Driver.drivers = [];

function gossip(input) {
    var addDriver = route => Driver.drivers.push(new Driver(route.split(' '))),
        drive = () => Driver.drivers.forEach(driver => driver.drive()),
        doneGossiping = () => Driver.drivers.every(driver => driver.heardItAll()),
        gossip = function() {
            var driversAtStop = {}, gossipsAtStop = {};
            Driver.drivers.forEach(function(driver) {
                var stop = driver.getStopName();
                if (!gossipsAtStop[stop]) gossipsAtStop[stop] = {};
                if (!driversAtStop[stop]) driversAtStop[stop] = [];
                for (var gossip in driver.gossips) gossipsAtStop[stop][gossip] = true;
                driversAtStop[stop].push(driver);
            });
            for (var stop in driversAtStop) {
                var drivers = driversAtStop[stop], gossips = gossipsAtStop[stop];
                if (drivers.length > 1) {
                    for (var gossip in gossips)
                        drivers.filter(driver => driver.id != gossip)
                            .forEach(driver => driver.receiveGossip(gossip));
                }
            };
        };
    input.split('\n').forEach(route => addDriver(route));
    var minutes = 0;
    while (!doneGossiping() && minutes++ <= 480) {
        gossip();
        drive();
    }
    console.log(doneGossiping() ? minutes : 'never');
}
$.get('input.txt', gossip, 'text');