Hello sir,
After I married my Swiss man, it took me about 2 months to get my B permit, although I had to convert from another canton where I had a previous B permit under other circumstances, so I understand there was extra lag time. It was very straightforward, other than the cantons bickering between each other, as soon as the paperwork as all in order. As long as you prove you're married and living together they're happy to let you be a pretend Swiss person!