In my mind, a bivy alone would be very confining and uncomfortable for any kind of wet or snowy weather of the sort you'd get in Spring/Fall. As another poster said, it isn't a shelter. It's only a bag you can crawl into.

The idea of a used tent is attractive to me as a 'tent guy', but it may not be lighter than the tent you say you are abandoning, so unless your current tent is somewhat heavy, there's no point in duplicating what you already have.

So, for the criteria you've mentioned, ($150 or less for everything, shoulder seasons, lightweight) I'd say a tarp/groundcloth combo you could set up with trekking poles (assuming you have them) would probably meet your needs best. If you go this route, learn several pitches for the tarp and practice them in your yard. Tarps are not tents and require some skills to use properly in bad weather, especially wind.