From what I see, the God of the Bible only allows sex within permanent relationships. The exception being between a person and a slave, which the slave could eventually be given freedom and leave the committed relationship. I recommend having a conversation with your significant other and asking him/her if they will be in a relationship with you and not sleep with anyone else. Get married. Make sure both of you are tested for HIV/ AIDS. I know of two stories where a husband didn't tell his wife that he had HIV and ended up infecting her. This same scenario can happen in a homosexual relationship.
As a LGBT person, you may have been taught that you can't be yourself then realize that the Bible has been changed to forbid homosexuality. This is true but there still are restrictions on individual Christians. Paul says this: "but I am subduing and enslaving my body lest I have preached to others and I my very self (qnom) shall be rejected" (1 Cor. 9:27). Qnoma refers to a person's individuality or individual self. Some people struggle with promiscuity, anger, et cetera; of which these individuals need to know how to control themselves. Don't get in the mindset that because there are homosexual relationships in the Bible that you can sleep around as a Christian. No. The Bible forbids fornication, which Alexander Oraham defines the Aramaic word zanyutha as: "fornication, unlawful sexual intercourse on the part of an unmarried person." This would include sex before marriage, promiscuity, incest and prostitution (Jn. 8:41; 1 Cor. 5:1; Rev. 2:21). The Bible also forbids adultery. If fornication doesn't mean "sex before marriage &/or promiscuity" then why would someone get married? That would limit their sexual partners.
Paul taught that to avoid fornication, a man shall take a wife and a woman shall take a husband (1 Cor. 7:2). Later in the chapter, Paul said that if a husband is bound to a wife, don't seek a divorce and if he was divorced from a wife, not to seek a wife (1 Cor. 7:27). Elsewhere, monogamy is the ideal in the New Testament (1 Ti. 3:2,12; 5:9; Titus 1:6). Since God's ways are equal (Eze. 18:25,29), we can see what God requires of gay people by analogy. Lesbian, gay and transgender Christians (I will get to bisexuals later) should take a partner to avoid fornication and not seek a divorce for frivolous matters. If they get divorced then they should remain single or be reconciled back together (1 Cor. 7:10-11). That is why it is very important to marry a Christian you are attracted to and has good morals. You may need to get to know the person by observation, questioning and asking others about his/her character.
For bisexual people, they may need to deny a part of themselves. I want to stress the word "may" because I don't know. It appears that the New Testament only allows for monogamy. Polygamy is also inherently unequal. One person may think "Why should s/he get to sleep with two people and I can only sleep with one person?"
Nevertheless, Christians also get teaching from the Old Testament. The Old Testament contains bisexuals such as King David and Jonathan and Judith and her maid. Maybe polygamy is allowed for bisexuals. A permanent relationship would still be a must with a limitation of sexual partners in a group to likely three or four.
If an additional partner is allowed, then the following could be the scenarios. Probably the best decision if one person in a marriage is bisexual, is to find another bisexual to be in the relationship. That way the relationship is equal and each individual has two people to sleep with. If both people in the marriage are bisexual, then that could lead to the possibility of another woman and man to the marriage, with a total of four people having a covenant of only sleeping with members in that group. Nevertheless, a bisexual husband could also get married to a gay guy. This would fulfill the permanent relationship for the gay guy and the sexual or emotional need of the husband. A similar situation would be if the wife was bisexual, she could marry a lesbian. Though it would be unnatural for a lesbian or gay guy to sleep with the opposite gender, that doesn't mean that s/he won't if any jealousy arose between any of the partners in the relationship.
I know there is a lot of temptation out there and you can fall in love with other people but promiscuity is very dangerous. If someone else wants to sleep with you then you can say that you can't because you are in a relationship. It may help for those in a relationship to allow each other to look at another person's private parts without any exchange of bodily fluids or sex. This would include looking at naked photos on the internet or seeing someone naked in person. Sometimes the best way to get rid of sexual lust is seeing a naked person. This can actually prevent cheating.
I know looking at nude people that aren't your spouse is controversial, but there is some Biblical support that seeing someone naked is okay with God. God didn't have a problem with people seeing the naked prophets Isaiah and Micah (Isa. 20:3; Micah 1:8). The Bible also mentions that Petros (Peter) was fishing naked (John 21:7). Peter's companions would have also been naked. Fishermen would fish naked because they would have to dive into the water to pull their fishing nets out of the water. Fishing was also a dirty and smelly job and could require the cleaning of clothing. Thirdly, there were also the naked games where the competitors competed naked. And fourthly, there were (& are) professions where someone sees someone else's nudity (i.e. Roman soldiers, officers, doctors, baptizers, etc.).