Hello AndreasK
Taking a bicycle on EC train is not an easy undertake, you might find your spot occuppied by tons of luggage.
It is possibly easier (and less stressful) to travel with the IC2 to Lugano and then using RE80 train for Milan. But, this trip cannot be done with an EC train ticket on the Italy part.
Therefore, when travelling with a bicycle, it is advisable to get first the bicycle ticket & reservation and then the ticket for oneself. Otherwise you end up in the situation that you have got a train ticket but not bicycle space…
Kind regards,
Roland