Bivying used to be regarded as a desperate act that you'd do in an emergency. In these circumstances a large polythene bag would serve as a make do shelter. Very cheap simple and pretty awful.
In more recent years bivying has become more widespread in the outdoor adventure arena and purpose built kit is now available. A comfortable bivy is a fine art that requires both forward planning and personal discipline. Even with the most expensive kit available, there is still a very fine balance between surviving and actually enjoying the experience.
Your question has all of the hallmarks of inexperience which in some respects is commendable, however I don't recommend bivying in winter as your first experience. There's a huge learning curve, usually born out of a bit of suffering so best get it out of the way before winter comes and it actually becomes important.
Cheap bivi bags are most likely to be made from heavyweight non-breathable fabrics, whereas expensive ones will be made from lightweight breathable materials. There's also likely to be a halfway house that has a durable fully waterproof ground sheet and a breathable upper. Generally you get what you pay for, these are the criteria that will attract a higher price tag, (in no particular order):
- Reduced weight
- Small Pack size
- Extra features such as a pole/hoop, insect mesh.
Ultralight bivi-bags with minimal luxuries are intended for the climbing / mountaineering / extreme enduro market where having to bivi is a necessity rather than a pleasure. These are made from high performance materials that offer both high breathability low weight and small pack size but are likely to not be particularly durable. These are likely to be top of the market price wise.
Cheaper alternatives exist for the outdoorsman where weight and pack size are not so crucial, these are usually made from heavier and more durable fabrics and might also offer luxuries such as insect meshes and poles.
Budget bivi-bags will be similar to the above but likely to have a fully waterproof groundsheet. This will have the effect of reducing the breathability of the bag and cause increased condensation, not really a great idea in winter. Damp insulation == cold.
Without knowing what your intended activity is it's difficult to be any more precise, so base your decision on budget and durability versus weight and performance.