BDSM stands for bondage/discipline/sadism/masochism. The term can refer to the subculture of people who are interested in dominance/submission and sadomasochism, or it can refer more simply to actions of a couple who incorporates some dominatrix/submissive role-playing as a part of their sexual relationship. Needless to say, the Bible does not mention BDSM, whether as a part of sexual relations or separate from them.
In regards to the “marriage bed” (Hebrews 13:4), the Bible does not give many restrictions to what a married couple can do sexually with each other. Beyond adultery (threesomes, swapping, etc.) and pornography, which the Bible clearly and explicitly identifies as sin, a good principle seems to be the “mutual consent” mentioned in 1 Corinthians 7:5. If a husband and his wife are in full agreement, with neither being forced or coerced, God has given married couples freedom in regards to what takes place in the “marriage bed.” Could this freedom include black leather costumes, non-violent bondage, and role-playing? There is nothing in the Bible that explicitly restricts such activities.
With that said, there are definitely dark aspects to BDSM in which a Christian should have no part. Receiving sexual pleasure through the giving or receiving of pain is not in agreement with what the Bible says about sex. Sex is to be an expression of love, affection, passion, gentleness, selflessness, and commitment. Sex is to be the literal/physical expression of a married couple being “one flesh” (Genesis 2:24). To bring pain, degradation, or humiliation into the sexual relationship distorts what it is supposed to be, even when such actions are consensual. The more extreme aspects of BDSM reek of Satanism/paganism and are definitively ungodly and perverted.
In regards to the BDSM subculture, the need to dominate and/or be dominated in a relationship, whether sexual or non-sexual, may reveal a psyche in need of being redeemed by God through Jesus Christ. Jesus Christ died to set us free from sin and its consequences (Luke 4:18; Galatians 5:1). Jesus Christ always demonstrated servant leadership, not dominance, in His relationships with others (John 13). The need to dominate and the desire to be dominated are spiritually unhealthy. Even if some “innocent” or fun aspects of BDSM are allowable within the context of marriage, the vast majority of what takes place in BDSM is absolutely not Christian or Christ-like in any sense.