What is the Biblical basis for the idea of accepting one's "station" in life?

I wouldn't say that the Bible says you should accept your station, but Jesus promised/guaranteed that those who are faithful in small things will be given more. Often times people give up before becoming powerful at something and they move on to something else. Making your station as powerful as it can be is the first step to getting promoted by God into greater responsibility.

When it comes to people as a "station", Christians understand that all people have potential that is defined by being created in God's image, and that they want that potential to come to fruition. This is a good aim, but not entirely in line with the teachings of Jesus. If people don't want to fulfill their potential we should let them make that choice.

Marriage is different. Marriage is a covenant, not a contract, that can only be dissolved if adultery is committed.

Solomon wrote about this in Ecclesiastes:

Ecclesiastes 9:5 through 11

For the living know that they shall die: but the dead know not any thing, neither have they any more a reward; for the memory of them is forgotten. Also their love, and their hatred, and their envy, is now perished; neither have they any more a portion for ever in any thing that is done under the sun. Go thy way, eat thy bread with joy, and drink thy wine with a merry heart; for God now accepteth thy works. Let thy garments be always white; and let thy head lack no ointment. Live joyfully with the wife whom thou lovest all the days of the life of thy vanity, which he hath given thee under the sun, all the days of thy vanity: for that is thy portion in this life, and in thy labour which thou takest under the sun. Whatsoever thy hand findeth to do, do it with thy might; for there is no work, nor device, nor knowledge, nor wisdom, in the grave, whither thou goest. I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.

As I read this it saying that one should live life the best he knows how, because once you die you have no more opportunities to change anything.

Paul also gave us some insight into this in his letter to the Phillipians:

Philippians 4:11 Not that I speak in respect of want: for I have learned, in whatsoever state I am, [therewith] to be content.

The words of Jesus seem to cover the situation better than any:

Luke 20:25 And he said unto them, Render therefore unto Caesar the things which be Caesar's, and unto God the things which be God's.

Matthew 13:22 He also that received seed among the thorns is he that heareth the word; and the care of this world, and the deceitfulness of riches, choke the word, and he becometh unfruitful.

Matthew 12:35 A good man out of the good treasure of the heart bringeth forth good things: and an evil man out of the evil treasure bringeth forth evil things.

Mark 10:21 Then Jesus beholding him loved him, and said unto him, One thing thou lackest: go thy way, sell whatsoever thou hast, and give to the poor, and thou shalt have treasure in heaven: and come, take up the cross, and follow me.

You may see a different message, but from my understanding of these and many other Scriptures, is that the real purpose in life is to assure your eternity and all else is futile, but that does not in any way say that you should not seek to better yourself when possible. But as in the case of the rich man Jesus wanted him to share his good fortune with others, the part about selling everything and giving to the poor was to find where his true treasure was.

Let me leave you with this thought; Jesus could have had all the riches or the World and all of the perversity that goes with it:

Mat 4:8 through 10

Again, the devil taketh him up into an exceeding high mountain, and sheweth him all the kingdoms of the world, and the glory of them; And saith unto him, All these things will I give thee, if thou wilt fall down and worship me. Then saith Jesus unto him, Get thee hence, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve.

About my life situation (or anyone's), I may have to stay at this job not so much for the job but to share my faith with everybody at work. Why then did God called me when I had this job. But if I get a better job, whatever. The Bible says 1 Corinthians 7:17-24

Nevertheless, each person should live as a believer in whatever situation the Lord has assigned to them, just as God has called them. This is the rule I lay down in all the churches. Was a man already circumcised when he was called? He should not become uncircumcised. Was a man uncircumcised when he was called? He should not be circumcised. Circumcision is nothing and uncircumcision is nothing. Keeping God’s commands is what counts. Each person should remain in the situation they were in when God called them. Were you a slave when you were called? Don’t let it trouble you—although if you can gain your freedom, do so. For the one who was a slave when called to faith in the Lord is the Lord’s freed person; similarly, the one who was free when called is Christ’s slave. You were bought at a price; do not become slaves of human beings. Brothers and sisters, each person, as responsible to God, should remain in the situation they were in when God called them.

About cultural status, we need to fear God in any situation. Remember Joseph, he was an Israelite then became an Egyptian but was faithful to God. Just like the Israelite midwives fear God more than the Pharaoh (Exodus 1:19).