'Do my bed' is wrong.
As a learner of English, you would definitely get 'do my bed' marked incorrect. It would be seen as an error, and you would lose points in a test for writing or saying 'I do my bed' instead of 'I make my bed'. If you were to say this, people would correct you.
That said, there might be the odd occasion when you might hear this, especially if making beds is one of a regular set of tasks which someone does as part of their job. For example, if two members of a hotel's staff have to make the bed, sweep the floor, clean the bathroom and refill the tea tray, one might say to the other, "You do the bed and the floor, and I'll do the bathroom and the tea tray". In this situation 'do' stands in for all the other more specific verbs, and it reflects the idea of 'do + a particular task'.
[In other contexts, 'do my bed' can also have other meanings. For example, if you've decided to paint all your bedroom furniture pink, you might say 'I've painted my wardrobe and bedside table pink, and tomorrow I'm going to do my bed" (meaning 'paint it'). Context is everything]
Those are rare exceptions, however.
PS As I was writing this answer, I had the words of another italki member ringing in my ears. A teacher of English from your country recently said to me "Stop bloody confusing people!" She gets angry when native speakers of English tell learners about exceptions, unusual uses of language or (worse still) regional variations. In her view, learners of English should be told only the 'correct' language which they need to pass exams. Maybe she's right. OK, here it is:
The basic answer to your question is "It's a big mistake". Don't say it.