BTDT. I started dating WH#2 3months after filing for D from WH#1. The D took 2.5yrs and WH#2 was by my side the whole time. He was also a BS so I thought he understood how I was feeling.
In retrospect I wished I had now waited before getting involved with anyone else. I wished I would have taken that time to get my own life in order. I knew I wanted the divorce and would never take XWH#1 back again. It did make my D harder because it infuritated XWH#1 that I was dating, then let WH#2 move in about a year later. It was at least 6 months before I introduced him to my children and then another 6 months before I let him move in with me. It did make the divorce easier as far as having someone there for me (I had no family anywhere near me)and his family loved me and my children. It also made me get to the indifference stage much sooner than I would have had WH#2 not been there. We married 3 months after the D was final.
What it didn't do is allow me time to grieve my XWH#1 and my first marriage. It also did not give me time to really live on my own. WH#2 looked like my KISA and acted like it from the start. I had my rose-colored glasses firmly in place for far too long and failed to see all the red flags that were blazing in front of my face. I thought that I had did everything right when in fact it was all just a mirage of my own making. I couldn't see the forest for the trees so when DDay#1 hit, I was devastated. We had only been married for a few years and he had been carrying on a LTA with an old GF that he had before we started dating. I am not sure if he continued to see her after we started to date or not. We lived about an hour apart at the time and I didn't allow him to spend the night with me when the kids were here, so for that year we only saw each other every other weekend and not at all during the week.
Please take this time for yourself before you start another relationship, especially if you and your WH are still living together. Be sure you are not jumping from the frying pan into an oven. Our pain makes our vision obscure to the point we sometimes overlook things about a new person that we would otherwise see. (((HUGS)))