Cost to get to the Alps & back in a car is around £500, depending on your fuel economy, which method you chose to cross the channel, strength of the £ to the € & the oil price (£160 chunnel, €190 tolls, ~£200 fuel last year)
Flying will cost around £200 with your bike, plus transfers to the resort (anywhere from £50-£200).
Eurostar doesn’t go direct to the Alps in summer, meaning a train & station (from the north to the south of the city iirc) change in Paris, with your bike.
FWIW I’m going twice this year; flying one time & being picked up by the guiding company and driving the second.