The answer is, as often is the case...sometimes.

There's a concept in Jewish law about foods that require Jewish involvement in their making (sometimes, only Jewish involvement) by Rabbinic decree. This includes most significantly cheese and wine. At one point bread and oil were on this list too, but these decrees were softened/rescinded over time. The exact legal details of this process are not terribly important. But because written material from Medieval Jewish communities is discussion of Jewish law, it means that those legal texts will give us a window into baking practices.

As background, there are basically three types of bread discussed in legal texts on this. First, "Jewish bread", which is bread baked either in a Jewish bakery or by a Jewish individual making bread for their household. Second, "baker's bread", which is bread baked by a non-Jewish bakery for sale. Third, "gentile bread", which is bread baked by a non-Jewish household. I also should note that I'm no expert in historical bread-baking, so I'm a bit hamstrung in my ability to put this information into the context of European bakeries in general.

It seems from the Medieval Jewish law codes that baker's bread was commonly eaten, and that in many places no Jewish bread was available. But it also seems to be the case that in some places there were Jewish bakeries, so sometimes Jews did have a Jewish bakery.

One such formulation is the Tur, a law code written by Jacob ben Asher in the early 14th century. He's useful because he grew up in the Rhineland, but moved so Spain, so in theory when he speaks to economic or social reality he's not just talking about one particular place. In discussing the prohibition (YD 112), he notes that "in most places of our exile there is no Jewish baker available". The compiler Yosef Karo (16th century, who wrote in Israel but had spent much of his life moving around the Mediterranean following the expulsion of Jews from Spain and Portugal, which happened when he was a small child) puts it as "there are places where people are lenient on this matter, and purchase bread from non-Jewish bakers in a place where there is no Jewish baker", which makes it sound like no Jewish baker available was a common, but not universal, circumstance. Moshe Isserles, his Eastern European contemporary, notes that some places permit non-Jewish baker's bread even if there is a Jewish baker available. He also says that when no baker is available at all one may eat gentile bread, "and this is the custom".

Putting all this together, it sounds like there were places that had a Jewish baker, and this was not an uncommon circumstance. In some, but not all, of those places Jews would only eat bread from the Jewish baker (but in others they'd eat non-Jewish baker's bread too). But in many places there was no Jewish baker, and people availed themselves of lenient positions in Jewish law to either permit non-Jewish baker's bread, or bread from a non-Jewish householder when no baker was available at all (which sounds like a circumstance that's rare, but not unheard of, but in literature like this it's hard to really know.

If you're curious about the ramifications for keeping kosher--until relatively recently, bread was "presumed kosher", i.e. the only kashrut issue was the above issue with eating bread baked by non-Jews. If bread was adulterated (which was often illegal), it was with inedible substances, not with products that would be problematic kashrut-wise. Modern industrial production (and cheap animal products) has changed this, and nowadays Jews who keep kosher generally only eat bread that's somehow overseen to make sure it's kosher (though most do eat bread from non-Jewish bakeries, at least in most circumstances), since it's really possible that non-kosher products would end up in bread. Still, the amount of supervision isn't that high in bakeries for this reason. And even as late as the late 20th century people needed to be convinced of this, and in some places bread still is presumed kosher.

I am unaware of anything suggesting that Jews used a different miller than everybody else. My guess is that mills were expensive enough to preclude this, and there's no reason in Jewish dietary laws why this would be needed (except for Passover perhaps). I believe there were Jewish millers on occasion, but that's a topic I'd have to do more research on.

Also there aren't so many kosher delis anymore (in the sense of actually following Jewish dietary laws), but that's a separate topic around changing food tastes and religious practice among American Jews.