I would write or say: "I was surprised to run into Mr. Wang at the bus station," or a version with the word "surprise" if I were speaking to someone who I wanted to maintain a bit of formality with. In my opinion, saying "out of the blue," at least in your example, is more informal and I would say that if I were just chatting with friends or something, but not if I were speaking to someone who I don't know so well, or who I only knew in a formal context.

It is a common phrase and is considered to be more idiom than slang. The phrase gives a picture of something falling out of the sky - "out of the blue". The first phrase you use should be "Surprisingly, I ran into Mr. Wang in the bus station." It would mean the same as "Out of the blue", but using the "out of the blue" makes the sentence more emphasis and color. If you want to really give an impression of being very surprised, then "out of the blue" is better.

Both "run into (someone)" and "out of the blue" are idioms and both express the notion that an event occurred which was definitely not planned. When I run into someone I am not usually surprised to see someone I know around my small city. If I went to a distant and remote place and ran into someone I knew, that would be out of the blue; I would be very surprised. I hear "run into" a lot, I hear "out of the blue" rarely and it has variations like "a bolt from the blue" and "out of the clear blue sky".

If you define slang as new words, then this isn't slang. The phrase has been used for a long time. You have it correctly above. Both sentences mean the same thing and neither is better than the other.