If you are only at the dating stage with the person, I would say, "yes, tell them." But please do make sure you are safe. If the person proves to be anti-LGBT before you even tell them about you, then just walk out. Don't risk your safety. You don't owe it to them to come out and put yourself in danger if they are aggressive.
I recommend that bisexuals tell their partner very early in the relationship that they are bi.
There is no way you will be able to hide who you are if the relationship grows into something more.
You won't magically become straight.
It is a lot easier to be honest when you're just dating someone than when you're emotionally involved and married with three kids.
And your secret will eat at you.
Being bi is part of who you are.
No one should have to hide who they are when they are at home.
You deserve a safe place where you can be yourself, free of judgment.
You can't hide from yourself in your own house.
If you are already married, then it becomes more or less tricky depending on your spouse.
However, I would insist that you do not cheat. Cheating is never the answer.
Your partner doesn't deserve that—especially if you weren't honest with them. They can't read your mind. They don't know what's going on with you or what you're going through.
Whether this is just dating or you are married, I would suggest trying to figure out if your partner is favorable to LGBT people first.
If you are only at the dating stage and the person hates on LGBT people, break it up now!
You deserve someone who will love you as you are.
Don't even bother.
You will meet someone who accepts you as a bisexual.
Dating someone who hates on your kind will only lead to frustration and self-hatred.
You deserve so much more!
You do not owe it to anyone to stay with them if they hate on you and who you are.
If you are married though and your spouse is homophobic and biphobic, you are stuck in a situation where you need to consider whether your marriage matters more to you than your orientation. That choice is yours, and only you know what is right for you.
However, always remember that you did nothing wrong!
And there is nothing wrong with you!
If the person (be they just a date or be they your spouse) hates on you for being bi, they never deserved you to begin with.
Though it may come as a shock to them at first and their reaction might not be the one you hoped, they will get over it and accept you once they've processed this new information.
If they don't—and in some cases, it can lead to heartbreaking insults and complete disdain—then remember that you did nothing to deserve to be treated that way. Everyone deserves respect.
Being bi doesn't mean you are a cheat. Straight people also do feel attraction for people outside their relationship. If they claim they never look at other men or women (including celebrities), they are lying.
You have done nothing to deserve hatred.
Being bi isn't the end of the world. And being married to someone who is bi isn't the apocalypse.
I hope this helped. If you have more questions, send them to ASK A BI.