What has worked for me and what I suggest is to keep your running gear together in one place.
If you're using headphones to listen while you exercise, put your fitbit and your headphones in the same place every time. Then when you grab your headphones, you see the fitbit and remember to put it in your pocket.
I've been running outside in the cold, so I have a small box where I keep my heart rate monitor, the strap for the heart rate monitor, my phone protector case, my running gloves, and my cadence sensor. When I gear up to go running, I open the box and put on what I need for that morning. My headphones don't fit in my box, so I just keep them nearby.
So, this is something you can try. If it works, great! If it doesn't work, then try tweaking your environment some other way to help you remember.
- John