Moving your budgie's cage around isn't a problem at all. I move my budgies' cages frequently and they love having the change of scenery. 
Would you be able to give the budgie out-of-cage time and tame it in the bedroom but have its cage on the wall that is about 4-5 meters from your kitchen? I don't recommend keeping it in the bedroom at night because even with the cage covered there is a chance of a draft. Additionally, it's best to leave a portion of the cage uncovered and to use a night-light in the room with the budgie so it doesn't suffer from night frights.
Take a look at this link for information on helping to keep your budgie warm.
http://talkbudgies.com/articles-general-budgie-info/314674-keeping-budgies-warm-winter.html
Would you be able to give the budgie out-of-cage time and tame it in the bedroom but have its cage on the wall that is about 4-5 meters from your kitchen? I don't recommend keeping it in the bedroom at night because even with the cage covered there is a chance of a draft. Additionally, it's best to leave a portion of the cage uncovered and to use a night-light in the room with the budgie so it doesn't suffer from night frights.
Take a look at this link for information on helping to keep your budgie warm.
http://talkbudgies.com/articles-general-budgie-info/314674-keeping-budgies-warm-winter.html