What were some general immediate reactions to this by the population, immediately following the protests? Outrage (how dare they), Apathy (who cares it's only a bus)...?
Segregationist citizens of Montgomery began to spread rumors about Parks shortly after her arrest: that she was from out of town, she was really Mexican, she was a Communist, even that she had a car so she didn’t need the bus.
Rosa Parks was arrested December 1,1955. The Bus Boycott began Monday, December 5, 1955. Other reactions eventually included the arrests of the boycott leaders, and the bombing of the homes of Martin Luther King (a little known 26 year old Minister of the Dexter Avenue Baptist Church in Montgomery and E. D. Nixon a leader of the local Montgomery NAACP chapter.
Most sources appear to be American, did this event get any attention outside of the US?
I could not find any international reaction to either Rosa Parks action or the bus strike which followed. In 1963 Martin Luther King was named Time Magazine's Man of the year, and in 1964 at the age of 35 was the youngest man ever to be awarded the Nobel Peace Prize. Organizing and leading the Montgomery bus strike was his first actions which put him on that path.
Which arguments were used to discredit the protests, beyond the well-known allegations of the protest being planned ahead of time and Parks being a Communist?
Rosa Parks is civil rights royalty. To many her actions kicked off the most effective time of the American Civil Rights movement. Given that there are a lot of myths on both sides of Rosa Parks protest. As the segregationalists sought to discredit her; desegregationists sought to paint a narrative which portrayed her as just a tired seamstress who had refused to give up her seat in the spur of the moment. The truth was a little more complicated.
Rosa Parks was a long time civil rights activist when she refused to give up her seat on that bus, she was an officer (secretary) of the local chapter of the NAACP and had been a member of that organization for a decade. Parks was attending the Highlander Folk School, "an education center for activism in workers' rights and racial equality in Monteagle Tennessee", just a few months prior to Dec 1, 1955. She had also been kicked off the same bus by the same bus driver several times before for the same offense. Beyond these facts the other truth was that it took incredible courage on the behalf of Rosa Parks. It was incredible dangerous for African Americans to oppose the status quo in Alabama. August of that same year Emmett Till, a 14 year old boy had been abducted from his home and murdered in Tallahatchie County, Miss for whistling at a white woman. For Rosa Parks to not only oppose segregation but to allow herself to be the face of that opposition in 1955 it was an incredible dangerous and courageous act.
It's also true that the bus boycott had been long planned prior to Rosa Parks. That the NAACP had been waiting for someone who they believed to be a creditable sympathetic face of that protest. Rosa Parks was that person.
Rosa Parks Reaction
Community leaders were waiting for the right person to get arrested, who had no record, would prompt the action of the African American community, and who would agree to fight in court. A fifteen year-old girl, Claudette Colvin, was arrested for not giving up her seat and was initially thought to be someone E. D. Nixon could fight for. However, she was pregnant and unmarried. Nixon explained later, "I had to be sure that it would be someone I could win with." Maybe it could be Rosa Parks. She was educated, worked as a seamstress, and had worked with the NAACP, taking interest in the Claudette Colvin case. She had just finished a workshop on race relations before being arrested in December 1955. She was well-respected member of the community.
As for being a Communist. That's actually not exactly far from the truth. The Soviet Union had been active in the American Civil Rights movement for decades.
Although not members, both Rosa Parks and her husband attended meetings.
In Howard Zinn's, "A People’s History of the United States" he makes the case that civil rights leader attending communist meetings in the decades prior to Martin Luther King was not unusual. That the Soviet Union was involved in organizing and funding the American civil rights movement for their own means from the early 1930's. Civil Rights leaders of that generation, saw nothing wrong with listening to their advice and taking their money to further their cause.
Some additional sources documenting Soviet involvement in the Civil Rights Movement.