My bi polar mother in law wants to move across the country to be closer to us. Do we support her decision?

Start asking lots of questions.

If you are embarking on a tour of duty fraught with danger, only proceed if you know the plan, can assess the risks & are willing to be signed up.

It could be just a passing wishful thought?

Or is it a formed plan (using logic) that being closer to family would be practical?

Or a manipulation attempt? To move in with you permanently but kindly requesting for "a little while.." as the first reply from Grandma1954 mentioned.

Your gut instincts will know.

This really depends on what she is expecting from you.

Do you know why she desires to move close to you?

Having her nearby will make things easier when she inevitably does need care, you won't have to deal with moving after a crisis or trying to manage from afar. People have mentioned the difficulty of separating from her friends and familiar surroundings if she moves but she may be acknowledging that in reality those have already eroded. I think the key to this working will depend on her ability to be as self supporting in her new home as she is in her current one, and your ability to establish firm boundaries.

Does she have children where she is?

I have seen this in my church. A spouse dies and the family of the surviving parent wants the parent closer because they live out of state. The problem is, and I had one man tell me this, he had no friends where his son lived. The son worked so Mr R was left alone. He missed his Church family. His neighbors of 50 years. Its hard to start over at 80. He died 2 yrs later. And there were others that did not adjust to the change and passed not long after the move.

I have BiPolar in my family. I love my two cousins to death but doubt if I would have them live with me. Neither medicate one is worse than the other. The manic side is bad in the one not so with the other. He just seems to keep more to himself. And I think he is manic when he calls me.

Seems like husband doesn't want Mom moving either. He, and it should be him, needs to tell Mom no the move is not a good thing. Not I "don't think" the move is a good thing but that its not happening. For a good reason, she is 80. She has friends. It will be hard to make new ones. At 80 she should not be driving in new areas. If she can even pass the test in ur state. She cannot live with you and she can't expect you to be her entertainment. You will be retiring, traveling and doing your own thing while u can. People like MIL u need to be very upfront to the point of being blunt. It won't work.

I am curious where your Husband, her son stands in all this, and if he speaks to her about it. Big moves are very major in our lives, a cause of much trauma to our systems. That is not made easier by loss of friends, if she has them, nor by age, nor by mental challenges. I would caution that it be made clear that moving IN with you, even temporarily is not an option. That is the road to disaster, the recipe for disaster.
It sounds as though your MIL is now recognizing she needs more support. In a loving family that is close, gets along well, such a difficult move makes sense. However, in one with many challenges, and dependent on assets and ability, a move into senior living, independent living, etc. makes much more sense.
It sounds as though both you and your husband may be afraid of this move, and I suspect that is not without good reason.
You cannot stop someone who is mentally competent from moving anywhere they wish, so there is that. What discussion has been had between your MIL and yourselves?

Well, you can't control what she decides to do if she is mentally competent. The question is: what is she expecting of this action? Is she just assuming you two will become her caregivers? Your husband must pose this question to her. Then, he needs to discuss it with you. And you both must be on the same page, whatever the decision is. Does your husband have siblings? They should probably be looped into this conversation at some point so that they are also on the same page and there are no surprises, disappointments or resentments.

You already have a taste of how she is...which will only become more pronounced and challenging as she ages. Please encourage your husband to read around on this forum the posts of others with bi-polar aging parents. They will definitely tell you to NEVER consider moving her in with you, even temporarily. I wish you both much wisdom as you broach this topic with your MIL.

Where will she live?
If she plans on moving in with you for "a little while"..."until I find a place"
I would probably say not. Or not until you find a place to move into.
Is she in a house now?
Has she looked at the housing in your area?
Would she consider moving into a "Continuing Care Community"? One where she can go from Independent Living to Assisted to Skilled Nursing or Memory Care if that is ever needed? If so she can take virtual tours and arrange a real tour at some later date.
BUT this is NOT the time to move across the country for no real need.
If she is doing well now where she is I would strongly suggest that she remains where she is for the time being.