Bear in mind

Bear in mind
 

Can we use it in the following context
I,ve always born in mind to write you.?

I've never heard it used that way, but it's not an impossible construction.

'Bear in mind' means 'remember' or 'keep in mind'. The following sentences work:

I've always remembered to write you.
I've always kept in mind to write you.

On the other hand, if you meant "have in mind" or "be on one's mind," these sentences work:

I've (always) had it in mind to write you.
It's (always) been on my mind to write you.

Thanks

By itself this sentence is strange.

The expression "bear in mind" typically identifies some fact or condition that will affect or should affect a decision or a course of action.

For example:
Ann: I'm going to walk home from work today.
Bob: Bear in mind that it's supposed to start raining this afternoon.
Ann: Ok, I'll bring my umbrella with me.

Maybe an attempt to translate into English "Siempre te estoy por escribir (pero no lo he hecho -- circunstancias del momento hacen que lo posponga)"