Bear in mind means to keep in mind. It is an idiom in English. Idioms are those phrases or sentences that are used commonly in spoken and would make sense to people with the knowledge about the language. It is colloquial in nature. It refers to "hold in one's mind' or "remember". It also means to allow for a certain possibility or plan for it. Thus it means taking into account. It means accepting to the truth or validity of a certain fact or point. It is a phrase that is commonly used some instances of the usage of this term are "bear in mind your capabilities before venturing into something", "it is good to bear in mind the strength of your adversary".
'Bear in mind' means to remember that there are other possibilities that might happen in any or in this particular situation. 'Bear in mind' (keep in mind) there is more than one solution.
Bearing in mind means keeping in mind. This is used when you are previsioning somebody