First feel the resistance in you to not feeling heard or to someone else drawing attention to them. Say to yourself "This is my resistance" This is the first step to awareness. Next, remove the word "always" because it trains your brain to not separate out things. (You have your way the other person has their way) There may be times she doesn't "always think she is right". (even though you may not be present during those moments :) )
Get specific. "Last Tuesday during our meeting I noticed I made a suggestion and instead of feeling like I made a contribution I felt dismissed to what you said instead..."
I would recommend talking to your supervisor directly but there is a step I would do before that. First, ask yourself, "who does she remind me of?" then feel into your body and allow yourself to remember in your past (usually early days of life) and see if her manners or way of being remind you of anyone - typically mom or dad.
If you get a yes and identify the person imagine they are in front of you. Then say to them what you really wanted to say back then that you couldn't. Notice if you feel stronger or weaker in your body. If you are using victim or blame language you may feel weaker. Try again if so with responsibility like language. For example, "Dad I notice you interrupt me when I want to share with you" or "I feel angry when I share something and then you ignore what I said and share what I imagine is something you think is even better. What I want is..." Hope this makes sense. The key is to feel the change in your body.
Our memory systems are powerful. When we resolve past incompletions we no longer have to attract people to give us the lesson again and again. Its how trauma works. It will recapitulate events over and over again until the brain get resolve.
I'll caution you about talking directly to your manager because in the corporate world there is little mercy these days. If you sense they are generally open to feedback then do it. Use language that is specific and non-blaming. (If you are making them wrong then their defensive maneuvers will kick in and you may not be able to get your needs met.)
If they are hostile then be sensitive to your wellbeing.
All the best to you.