I'll pass on what my teacher has told me, and a few things I've figured out. From what I can tell, there are no bowing principles that apply to every song in every style. There's a certain amount of individual choice by each player. Kind of like when to breath for singing or a wind instrument. Sometimes there's really obvious places to do it, sometimes it's what works best for you and your capabilities.

Don't take the "rule" part of these too seriously, by the way. It's just a way to separate the talking points, not a "do this or else" type thing.

Rule 1: Always start on a down bow. My teacher said that this is about the only hard rule in all of violin playing. It mainly matters when you have an orchestra - they like to see all the bows moving in unison.  In anything orchestra-like, you may have a conductor wanting you to use certain bowings specifically so things will look they way they want. If you're playing by yourself (or the only violin in a group) you don't need to worry about that. Music written for violin will generally assume you're starting on a downbow.  Music written for other instruments, you have to figure it out for yourself.

Rule 2: Use more bow.  This is (by far) the most often repeated mantra my teacher says. (Well, it was until I finally got the idea. ) You don't want to try to use the entire bow to play a note that's say 1/24th of a second long (a sixteenth note at 90 BPM), but you DO want to use as much bow as practical for each note, unless you're trying for a special effect of some kind.  The more bow you use, the better your tone will be.

Rule 3: You can slur faster than you can bow.  If you have several notes on the same string, and you need to play them fast, you probably want to slur them rather than change bow direction for each one.  (It depends on the style you're trying to play in, though - see rule 4).

Exercise to improve independence of right and left hand:  Play a long slow note, using the entire bow, on one string, and finger something else on another string (anything that is on one string will do. I used "Ode to Joy".) Hear the song that you're fingering in your head, but do NOT change bow direction or speed. (Change direction when you get to either end of the bow, of course.)  Warning: This exercise will seriously mess with your head at first.

Rule 4:  Changing direction makes each note more distinct, more independent of the ones around it.  Imagine. talking. like. this. to. punctuate. your. idea, versus talking in a smooth, flowing phrase.  At least in violin playing, both styles are legitimate, although certain songs and certain styles tend to accentuate one over the other.

Rule 5: When to change direction in your bowing has a lot more to do with what's coming up than what you're playing now. Especially if you're following rule 2 (use more bow), you're sooner or later going to run out of bow. You want to be near one end or the other if you're going to be playing a long note in the near future, and you don't want to start that long note heading towards the end of the bow you're almost at.

Rule 6: Two notes of the same length don't have to be played with the same amount of bow. Say you're in the middle of the bow, and want to be near the frog for that double whole note coming up in another measure or two. You can change direction for each note in those preceding measures,  playing short down bows for one note, and a longer upbow for the next. After two or three changes like that, you'll be near the frog, and then all you have to worry about is that you play the really long note on a downbow. Using more bow tends to make the note louder, which can be compensated for by using more or less pressure, but I've found it's not usually that noticeable. Moving up/down the bow that way AND compensating so that the dynamics are perfect is more of an advanced technique than I'm up to at this point.

Rule 7:  Don't worry about rules 3-6 unless you're having a problem. Practicing them is a good idea to build the skill, but outside that, don't bother with them if you don't need them. There are WAY to many things to worry about in playing a violin to be adding extra ones unnecessarily.