Turin Airport is correct entry point for Bardonecchia - airport is about 100 kilometers east and drive west on A32 autostrada through Susa Valley takes about 90 minutes in normal conditions, and normal conditions on that road in ski season means allowing margin for Friday afternoon and Saturday morning traffic that Italian ski week generates. Car rental at Turin Airport is straightforward with all major providers represented and car is definitley recommended configuration for this destination because ski area access and daily equipment logistics are significantly easier with own vehicle.
Train connection from Turin to Bardonecchia is one of better public transport options in Italian Alpine skiing - direct trains run from Turin Porta Nuova with journey time of about 90 minutes and Bardonecchia station is walking distance from hotel, which makes train correct solution for guests who don't want driving variable in winter Alpine conditions and don't need to transport large amounts of ski equipment. Ski rental in Bardonecchia is available and of correct quality so arriving by train without own equipment is viable configuration.
From Milan connection goes via Turin and adds about 90 minutes to journey - total from Milano Centrale to Bardonecchia by train is around three hours, which is manageable number for Friday departure and puts you in mountains beofre dinner if timing works. From Lyon on French side drive through Fréjus tunnel is about 90 minutes and is correct approach for guests coming from western direction.
Getting around Bardonecchia itself once at hotel is primarily on foot for town and ski area - center is compact and lift connections are walkable, which means car is useful for day trips to French side or to Turin but is not required for basic ski week programme. Absence of car dependency for main holiday activity is partiuclar quality of Bardonecchia that - fully car-dependent Alpine resorts where you drive to lift every morning create logistics overhead that compounds badly in bad weather, and not having that overhead is worth more than it sounds on mornings when conditions are difficult.