By dy and indoors, do you mean your garage??
If that's the case, be aware that a lot of concrete slabs in garages tend to emit some moisture through from the ground if it was not built with a moisture barrier (a plastic sheet/membrane) Most older garages were not built this way and there could be enough moisture emittance to cause the rusting you see. Similar applies to basements but to a lesser extent, unless you really have big moisture or water leak problems in it. Also, do not cover your bike with any kind of impermeable material like plastic sheeting as it will trap moisture against your bike and accelerate corrosion. An old cotton blanket will actually be better to use as it can breath and release the moisture coming from under the bike.
You might be able to get rid of most of that rust, if it hasn't damaged the chrome underneath it too much, by rubbing it with crumpled aluminum foil. I usually dip it in WD40 and it works even better. Do a search in the forum under maybe "crumpled foil" and you ahould find more information on how to do this.

Chombi