Little bit of water under plastic cover on my shimano shifters I've had my bike for a month or so and just gave it a clean. There is now a little bit of water trapped under the shimano shifters clear plastic covers. Is this a problem? Will it disperse eventually? Was going to ping off the covers but was not sure if they would go back on easily or the correct way to get them off. 

Any help appreciated, know very little about bike maintenance!
You don't need to worry about that.

There are nearly no components on your bike -- except for the hub and bottom bracket bearings -- that are sealed to be more or less waterproof. Most of the components are totally fine with water on or in them.

Especially for your shifters: their internals are mostly made out of plastic so no need to worry. As they are built in some half-closed way, there may be some water condensation in some corners, which is no real problem. The water may disappear as soon as the weather is warm enough and the bike stands in the sun for some time. It also may reappear, but as said, it's not a real problem, just some matter of optics.