If you are in a region where natural disasters are regularly occurring, bugging in and taking care of yourself is always a better option than getting on the road to a faraway location then turning around three days later to come home.
I live in an area that is not often ordered to hurricane shelters. Shelters are open for voluntary evacuees from mobile home parks or low ground prone to flooding. Mandatory evacuations tend to happen on the coast. For me, there is no reason to bug out for some heavy rain. I will however bug for a category three storm, but, it's a short hop bug I can make in less than an hour from packing to arrival at the hold up.
When I truly bug out it will be because the neighbors have been expelled from the shelters when the supplies run out and they have none of their own to survive. When they show up, I will be gone. That is the plan. When bugging out it is better to go sooner rather than later! There is no point in waiting for the shooting to start. I have a good sense about the neighbor hood and I know when I don't or won't feel safe.
But, for you, the first step to answering this question is to get lots of advice then stop doing what you are told and decide what is right for you. There are plenty of blogs and dot coms that debate the issues of bugging in or out. Read some of them. Read up on both sides. Then stop. Quiet your mind and decide what is right for you.
You need to come up with a plan. At this point, you have to come up with your own GOOD, get out of dodge, plan. Or, you need a good hunker down plan. Your home may be more defensible than any you could walk or drive to. You may be situated between a rock and a hard place and bugging out is your best option. Get a plan.