I had the same experience in my last job search. I only did a bachelors. Even with many projects on my resume that were completely data science focused, my response rate was almost zero for those types of positions. My response rate was very good otherwise. It's frustrating. Based on my conversations at data science/analytics meetups, my knowledge is greater than that of the average employed data scientist.

My suggestion is to get a job somewhere with a data science team, do a data science side project with company data, and demo it to the data scientists. That is probably your best bet to get a foot in the door.