Since a router in bridge mode works like a modem, do you need to even update it?
There are a number of reasons to update anyway. I assume, that behind the router/modem in bridge mode, you have some sort of security measure protecting yourself (like a firewall).
First are the features from your provider. If your provider suddenly offers new features like IPv6, your ADSL router may need an update. It may even be that your old router/modem only supports out-of-date protocols for connecting at that at some point, these are no longer supported by your provider (I've seen that with VPNs)
Second, it may be that your router/modem in bridge-mode is hacked and used as a stepping stone. Not to your own network (I assume that you have your border controls in order) but as part of a large DDOS attack, for example.
Of course, if your device is taken over, that is the ideal place to start a man-in-the-middle attack on your traffic.
There may be other reasons as well, but these should be sufficient.