Question: I'm planning to travel from Osaka to Tokyo and back, and since the ride will be long, I think it's the perfect time to make friends.

However, I'm unsure how the Japanese see this kind of behaviour - a stranger suddenly conversing with them who is a foreigner.

Is it considered rude? Is it a case-to-case basis?

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Additional info :

I can speak Japanese. I've been studying it for a year. I am at a conversational level but still not as good as locals and I may not know some words they might throw at me.

Answer: 
I haven't found Japanese as chatty as Europeans or Americans, but there are some friendly people who would want to chat with a foreigner. You won't know until you try. Old ladies and people with families tend to be the most chattiest -- young women and businessmen tend to be the least. There's a stereotype (that I've found to be true) that folks from Osaka tend to be much friendlier than those from Tokyo.

You should be aware that it's only 2 hours on the Shinkansen, which in Japan is not considered a very long train ride (some people have daily 2 hour train ride commutes). But still, you might strike up a conversation.

I'd suggest riding in the regular car (not Green Car), maybe taking the Hikari instead of the Nozomi, and asking to get your seat in the non-reserved section so you can deliberately sit near someone who looks friendly.
It is not rude as such, but unusual for strangers to talk on the shinkansen except to ask something specific like if it's okay to recline the seat (asked to the person sitting behind you.) Usually it's very quiet in there except for groups travelling together.

I live and work in Tokyo and take the shinkansen to and from Osaka about once a month. I am a visibly white woman but I don't have the usual apparel or luggage of a foreign tourist.

People take the shinkansen for the same reasons as a domestic plane flight. Some people are using it to take a fun and rare trip, others are commuting, some are going to weddings or funerals. It's my perception that most lone riders do not expect to talk with anyone, with the majority putting up some sort of barrier to conversation such as putting headphones on or closing their eyes. It would be rude to disrupt these people after they have already put up that barrier.

Otherwise, there is no harm in trying to talk to your seatmate, but I would test the waters first by saying hello and smiling when you sit down, then seeing whether they greet you back, just smile, or not even make eye contact.

Perhaps you could then ask them a question that gives them a chance to help you out. You could ask them which side of the train Mt. Fuji will appear on. How they answer will give you a clue if they want to talk more, and you can go from there.

I have ONCE in six years had a person sitting next to me spontaneously talk to me and we ended up productively chatting about where we are from, our jobs etc. for the whole trip back to Tokyo. He was a bubbly Osakan in line with the stereotype, and I felt he wasn't trying to pick me up but was just curious and wanted to fill the time. This was on the way back from the Obon summer holiday. He even gave me one of his many boxes of Horai pork buns as a thank you -- I guess he felt he could part with one. So you never know!