We enjoy bell peppers, and I have attempted to grow them unsuccessfully for years. I might get one or two small peppers. Most of the time they get blossom end rot. I have tried to adjust the soil and do all I could. I think it mainly has to do with the fact that I'm not a very routine person. I am more likely to water deep not very often. Everything else seems ok with this, but not the peppers. I have discovered the lunch box peppers. They are the small sweet peppers you see in the bags at the grocery store. They are prolific, mature fast and are ever bit as good as the bell. I will continue to throw a few bell pepper plants in each spring, because that's just the way I am. (never say die) But I will be planting these sweet little pepper plant for our family to enjoy. Happy gardening.
“We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses.” — Abraham Lincoln
I’ve had similar issues with bell peppers: they don’t want to set fruit and if they do they rot on the plant before they are near ripe. I try to water infrequently like you said (weekly and deeply until the monsoons start).
To add my experience to the mix, I also grow chiles every year and they grow great! No issues surviving, setting fruit, even drying on the vine! Morphologically, they are long and skinny; maybe that’s the difference? I bet, though, that it’s simply that the chiles I grow are more locally adapted to desert living and therefore able to withstand the abuse that the environment and I can dish out, but the bell peppers are adapted to some well-irrigated, fertile California soil.