I am a native speaker (U.S.) and have never heard anyone say "bolster up" for any reason. I would avoid it (unless you are working in the construction industry) and just use "cheer up".

The differences are subtle. Maybe a breakdown of the more literal meaning of the two phrases would help; to bolster something means to prop up or support something that is damaged, on the point of collapse maybe or otherwise deteriorated. For example bolstering up a leaning wall with wooden braces. So you have the image of something that, without the additional support, would fall down. Cheer up is a more positive phrase, 'cheer' is synonymous with 'joy', good spirits etc, as in Christmas cheer, so overall it's a much brighter image that the word cheer conjures up.

So, for those reasons I would say that to bolster someone up means to support someone who really is on the verge of collapse in some acute or chronic way and so is dependent on that support, or who needs support to get through a specific issue. To cheer someone up might be more appropriate if that person is a bit down in the dumps and would benefit from some positive contact, but might not be dependent on it. But those are subtle differences and in some examples might be reversed!

In general use, in the UK at any rate, to say cheer someone up is more common than to say to bolster someone's spirits.

i think you can use both interchangeably