I have 3 years experience in NICU, been trying to get into research with no luck so far. What is the best way to go from bedside RN to research RN?

Check to see if your facility has a Nursing Research Committee or Council. Participation in that would expose you to research and allow you to participate in activities to put on your resume. Also, look for CE opportunities or other education on research to demonstrate knowledge of and interest in the principles of research. You might also see if there are local IRBs looking for community participants.