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I'm not a professional but I've totted up my public playing for a year and so a little surprised to find it's 50+, consisting of 3-4 per month playing in bands for dancers or public entertainment at displays or for charity (mostly Playford, but some barn dances and ceilis), and 16-20 symphony/chamber orchestra concerts (3 symphony/chamber orchestras + ad hocs and occasional deputizing). Keeps me out of the pub, anyway!
You neglected the option for NEVER! I feel very sorry for my teacher who I have to pay to listen to me. Even my cats leave the room when I practice.
I play viola and violin. I'm 87 years old, a retired pharmacist and have owned a pawnshop for over 15 years. I've been violist in the Joshua Tree Symphony Orchestra for the past 6 years, have been taking violin and viola lessons every now and then to keep up my skills. Every week in the public areas of my pawnshop, I play piano, clarinet and viola trios. In addition I play cello/viola duets with a local artist. Occasionally we have string trios or quartets. Stanley Zarakov, Yucca Valley.

I checked "More than 50 times a year" since, as you said, "even busking is a form of performing in public."

My kind of busking isn't something I get paid for, but payment isn't the objective. Here it's warm enough 7-8 months each year to play in the garage, and that's where I go in the evening once hard-core practice indoors is done. Audiences vary. Some passers-by stop to listen, and there's the occasional visitor who wants to try out my instrument.

To all this, I wish I could add "about once a week" for scheduled, posted performances of small chamber works, but time constraints keep me from this right now.

I don't particularly enjoy performing in public (yet) but I know that it's good for me to do it. Let me rephrase that - it's great for me to do it. Nothing else makes me work as hard on pieces; nothing else makes me think so much about musicality vs "just getting the notes"; nothing else forces me to deal with adversity (shaky bows, bad notes, etc). I know that playing in public (and all the prep that it requires) will make me a better musician. Unfortunately, for adult students, there really aren't a lot of opportunities available.
I perform on average once a week, mainly due to my attendances at the local-weekly 'open mic' sessions. But I also play in a band and do some freelancing. Even after my short hiatus from gigs some years ago I found myself very nervous performing on the stage. Stuff goes through my head and I get the shakes. But I know this is the 'ego' and there was only one remedy for that, so I put myself in the 'deep end'. Over the past few years I have become known as the fiddler who plays along with any song. People now ask me to play with them even without a rehearsal of the songs. And some musos even trust me to perform with them at gigs without the rehearsal. It may only be a short spot for only 50 bucks, but the money is not the point. It's all about practising my craft...'for an audience'.
The motivation for that has come about because of my desire to perform my solo repertoire of light classical pieces and some gypsy pieces I have transcribed. I play them when busking, but there is a great 'little wood lined room' where they hold an open mic session.....this moment will come soon....no rush, it will be magic.
Assuming you mean on violin, but much more on piano, ca. 2-3x per month. Performing in public on violin is hard, but I do the adult recital 2x per year and then one or two other things.