Establishing a shrine in the bedroom? If one weren't able to have a proper room in which to establish a shrine, could the bedroom be a suitable place to put a statue of the Buddha ? 

As expressed by Lama Yeshe, sexual misconduct would include sexual activity if it is "near holy objects, such as the guru or the Triple Gem." (reference Taking the Mahayana Restoring and Purifying Ordination), thus reassessing how I approach the situation.

Considering this, would shrouding the shrine with a cloth or in a cabinet be sufficient to keep it there in such a place when not practicing ?

Many blessings to you.
First, you should keep in mind that rules are different for those on the monastic path than those who are lay practitioners. Monastics are not supposed to engage in any sexual activity (in most orders), but it is presumed that lay practitioners can engage in sexual activity without it being considered misconduct (so long as they adopt the right attitude). All you need to do is maintain a properly respectful attitude towards your altar.  This might involve covering your altar, buying a small folding screen to put in front of it, or even taking down your altar and putting it away when you are not meditating. 

It's worth keeping in mind that purpose of an altar is to create the proper mental state (attitude) for meditation and spiritual development. The altar itself has no intrinsic value or meaning beyond that which you imbue it with; it is more like a stepping stone or walking stick that helps keep you on the path as you move forward. An attachment to rites and rituals (sīlabbata-parāmāsa) is one of the Ten Fetters, so while it is important to maintain an attitude of respect towards any altar or image of the Buddha, one does so because it creates respect for the Buddha within, not because some external Buddha or external rule demands it. Follow your conscience and you will not go wrong.