Do bluetooth speakers for cars exist?

No, pretty much not. Most people just get a head unit with BT. 

If your current head unit has an aux input, you can get a Bluetooth receiver.

You can buy a gadget for $20 or so that plugs into cigarette lighter, receives Bluetooth and broadcasts FM on selectable frequency so you can use your car FM radio. Works well and sounds as good or better than broadcast FM.

I have the gadget mapman references and it works great, here is a link to Amazon where I got mine.

https://www.amazon.com/gp/product/B01DZKERVY/ref=oh_aui_detailpage_o06_s00?ie=UTF8&psc=1

Yes that is what I have also.  Works great.   Be aware if left plugged in and on when not in use it may cause some interference with some FM broadcasts.  Best to simply unplug when not in use.  

I bought a new Turbo Mini (to replace an older Turbo Mini) this year and like many newer cars it's equipped with blue tooth…it plays from my phone the moment I get in the car.

Plex is a great and affordable app especially for mobile music buffs who want to have their own music library and listen to it anywhere using smartphone/bluetooth anywhere including car, remote computer/browser, tablet, or on hifi at home.

Downside is you have to figure out how to set it all up and use it yourself. Definitely worth it though if you are a basic computer savvy music lover.

My most used music app these days by far. I use it at home on Amazon Fire, laptops/tablets/Iphone/bluetooth and mobile via IPhone/Bluetooth in car(via Bluetooth to FM broadcast adapter gadget) and while on the road.  Even on my computer at work via standard web browser and line in to a decent sounding table radio.   A Bluetooth speaker wold work very well there also but I manage to use what I have as long as the sound is decent.