Nearly every Jim Crow law provides for the establishment of separate facilities, structures, or areas for black and white people and many of them contain language that limits the movement of supplies across the race-line. Rosa Parks, as others in this thread have noted, was arrested and convicted for "refusing to obey orders of bus driver"

Under the city code of Montgomery, bus drivers had "the powers of a police officer of the city... for the purpose of carrying out the provision of [segregation of the bus lines]"

So, the simplest answer to your question -- at least insofar as the bus system in Montgomery Alabama is concerned -- is that the bus driver would be legally bound to order them to sit in the white section and the Courts would enforce that order as if it were a lawful order given by a police officer.

Which is pretty much exactly how nothing at all worked in the South.

The underlying purpose of the Jim Crow laws was to establish White Supremacy. After Reconstruction ended white-lead governments surged back into power and used their power to marginalize the black vote. They then used that power to enact Jim Crow laws which further suppressed black political activity and relegated black people to second class status. While stated goals for this are hard to find and differ on a state-by-state basis, it's illuminating to consider that white people were a racial minority in some southern states and a sparse majority in many others.

As we see later in the civil rights era, white juries -- and juries were often all white -- could refuse to convict white defendants of crimes they were obviously guilty of. While there is a real paucity of information on whites deliberately crossing the color line in the segregated south, the capricious nature of the enforcement mechanism in the case of Montgomery's bus lines combined with the double standards upheld by white southern juries would suggest that no criminal charges would be filed, much less effectively prosecuted.

Segregation existed not truely to separate whites from blacks but to keep black people down. While mass revolt against that social structure might have been effective or might well have occured (it occurs to me that if anyone tried it the Freedom Riders might have) I can't find evidence of it. Of course, absence of evidence is not evidence of absence.

There is, of course, a social element to this as well. The South was rife with slurs and epithets for white people who did not seem to share society's contempt for the black man. White northerners who opposed segregation faced violence and intimidation and southerners who did so had, at the very least, social consequences to deal with.

TL;DR: While technically they'd be in violation of the law, probably nothing because the purpose of Jim Crow was not to inconvenience white people.

OK, ok, ok. As we occasionally do when to satisfy the curiosity of you all, here is a tally of the thread, currently. In total, there are 47 top-level posts in this thread at the time I'm posting this(excluding this). Of those, there is ONE visible, a top-level warning by a Mod. That leaves 46 top-level comments which have been removed, for the following reasons (Relevant rules are linked, where you can find further discussion explaining the rationale of the rule):

• SIX Comments: Removed for being almost entirely a quote from another sources without providing additional context. This is a violation of our rule concerning Links and Quotations. Some of these might be primary or secondary sources which could be useful in sourcing an answer under the rules, but they are not sufficient on their own.
• FIVE Comments: Removed for being personal anecdotes - "My grandmother said [...]", "My father told me [...]". Personal anecdotes are not allowed to stand as sources in the subreddit, as per our rules, due to a number of issues discussed here. If that is what you want though, it is a great thing to use AskReddit, with a Serious Tag, for.
• SIX Comments: For lack of a better term... they were just useless. Example being the person who posted "IDK". These are comments which don't even try for an answer that might be useful, even on a sub less rulesbound than ours. See our rules on Digression and Clutter.
• FIVE Comments: These were removed for not meeting our requirements to be in-depth and comprehensive. For the most part they were just short simply not an exploration of the topic to the level we would expect, an example being this comment about Rosa Parks: "She had been seated in the colored section of the bus. When all of the seats in the white section were full, the bus driver ordered her to stand up to let a white person sit in the colored section. She was arrested when she refused." Is it technically incorrect? No. But one of the unofficial mottos here is that an answer isn't good simply for being right, but because it explains, and what that answer does not do is attempt an exploration of the greater milieu of race-relations in which the Rosa Parks incident occurred.
• ONE Comment: A follow-up question. To be clear, we do allow follow-ups, but we expect them to be in the 'sweet spot'. That is to say, if it is too unrelated, we'll remove and ask it to be put in a new thread, and if it is essentially just a restatement of the question, or else asking about something that is a core component of the question and an answer to the main question would be assumed to answer the follow-up, we remove that too. We allow them to stand when they provide an interesting angle that is related to the main question, but might provide for an interesting tangent.
• TWENTY-THREE Comments: Finally, the complaints and such. As stated here we welcome feedback, but simply ask it be put in a META thread, or directed to Modmail. When posted in an active thread, we generally remove it so as to not derail the thread. There is a wide range of comments in this category, from the super original jokers posting "[Removed]", to the new arrivals asking "What happened to all the comments?", and of course the guy asking "do all the mods here have their heads up their asses".

So there you go. Nothing that has been removed has even given us a moment of pause as to whether it might pass muster. It is a thread filled with very clear rules-breaking comments that were removed, fully half of which were commentary on the fact so many comments were removed. Needless to say, this just compounds the problem, which is why many who have posted those comments have received temporary bans.

Hopefully soon enough someone will provide us with a great answer, as usually does with popular threads, but it takes a little patience, and posting more rules-breaking comments doesn't help that. So please, sit back, relax, maybe grab a beer, and check back in this thread in a few hours.

Edit: To the report "1: every front page post i see has all comments removed and only mod comments. fix the sub please". That is a feature, not a bug. Given that frontpage posts had a 96 percent response rate last year, your statement is suspect anyways though.