Your mum will be arriving in the Non-Schengen part of the airport, so will need to pass through passport and security checks in order to reach the gate in the Schengen part of the airport, where the onward flight will depart from.
She should have been issued with both boarding passes at check-in in Durham. It's unlikely, though, that the gate number for the Bordeaux flight will be known, and it's always possible that this has changed. There are numerous departure monitors where she can check where she needs to go, and Schiphol is well signposted so it's one of the easier airports in which to transfer. There are several transfer desks (though they tend to prefer to wave you off to the blue KLM self-service transfer/connection machines) should she require assistance, but I think it's unlikely that she will.
Amsterdam is more-or-less a single terminal layout, but there can be large distances involved, depending on which pair of gates are in question. Most of the corridors have travelators, though, so it makes getting around less challenging/daunting.