So long as your paperwork: bikes ownership(title,licensing),passport/visa, home country drivers license, and insurance is valid and up to date, having foreign plates won't be a problem. I've had friends tour the US with a tourist visa on Austrian, Guatemalan, Honduran and German plates with no issues. Don't know about storing a bike though. Doubt if the Government cares if you're riding it or it's parked in a barn BUT there is a time limit. Don't know if it's six months or a year total(riding and storing). Likely that of your tourist visa. So long as "ALL" of your paperwork is 100% you shouldn't have a problem.
US Customs will have the info you need.