In other words, it sounds as if you've hit the limitation perimeter of the Betamid ($98), a single-wall, single-pole, floor-less tent that saves a bunch of weight (it's just over two pounds) but forces you to do without some niceties. Add the optional floor, and you're close to four pounds, which is close to tent weight.
The only other option, as you suggest, is to add a sleeping-bag cover. The best bet would be a simple Gore-Tex bivy bag, such as Outdoor Research's Standard Bivy Sack. But that weighs as much as the Betamid floor, and is expensive at $230. A good option: Mountain Hardwear makes a bag cover out of the same Conduit fabric that already wraps your bag. It's called the Conduit SL Bivy, and costs a more reasonable $109. The drawback: Two waterproof layers right next to you, which are apt to trap moisture inside the bag, or between the bag shell and bivy. And that could be bad, depending on conditions.
Bottom line: It's hard to find a place where price, weight and performance all intersect as neatly as you might desire. I suppose you always could by some 4 mil plastic poly sheeting, cut an 8X8-foot chunk, and wrap yourself in that when it gets nasty. That's what campers did in the good ol' days after World War II - take a chunk of military surplus waterproof sail cloth, and roll up in it when the rain fell.
Support Outside Online
Our mission to inspire readers to get outside has never been more critical. In recent years, Outside Online has reported on groundbreaking research linking time in nature to improved mental and physical health, and we’ve kept you informed about the unprecedented threats to America’s public lands. Our rigorous coverage helps spark important debates about wellness and travel and adventure, and it provides readers an accessible gateway to new outdoor passions. Time outside is essential—and we can help you make the most of it. Making a financial contribution to Outside Online only takes a few minutes and will ensure we can continue supplying the trailblazing, informative journalism that readers like you depend on. We hope you’ll support us. Thank you.