// Cancelling the event will remove the vanilla message but the action bar message won't work, it will only work if you delay it.

@EventHandler(priority = EventPriority.HIGHEST)
public void onBedEnter(PlayerBedEnterEvent e) {
   e.setCancelled(true);
   e.getPlayer().spigot().sendMessage(ChatMessageType.ACTION_BAR, TextComponent.fromLegacyText("This message doesn't work."));
}

// Working example

@EventHandler(priority = EventPriority.HIGHEST)
public void onBedEnter(PlayerBedEnterEvent e) {
    e.setCancelled(true);
    Bukkit.getScheduler().scheduleSyncDelayedTask(plugin, new Runnable() {
        @Override
        public void run() {
            e.getPlayer().spigot().sendMessage(ChatMessageType.ACTION_BAR, TextComponent.fromLegacyText("This message works."));
        }
    }, 1L);
}