re late june july for sleeping bags.
while there are all kinds of light, compact sleeping bags or quilts, as stated, a lot of them are pretty expensive. What I can say from personal experience is that for summer bike touring, unless you are high up where it will be colder, the places you want to ride in are generally going to be regular summer temps, maybe a bit cool at night, but not too much.
I have used a summer bag for ages, the same one for over 25 years. Its synthetic, could be a bit warmer the odd time, but then I always have a fleece with me, and tights or leg warmers, and warm socks, so really, every year when I think, "oh, its about time I looked at a new sleeping bag...." I then figure, what the heck, my old one is fine for what I need, the zipper is in perfect shape, and so why spend X hundred dollars on a new one?
It is fairly compact, which is nice, so my point is that there are plenty of economical summer bags out there that are not bulky, but will work for your trip.
Obviously look at bag options in outdoor stores, and make the decision on how much budget you have for camping gear, and go from there. Who knows what the weather patterns will be like for you at that time, but chances are they will be ok.
good shopping