There are a few triggers that makes a puppy wee on his/her bed.
He/she may be afraid to get off the bed, if you feel this is the case, or to see if it is, you need to remove the bed totally and put a towel down only so that he/she can go to the puppy pad easily without being frightened. Or else it will become a habit.
My little one is 17 years old, almost, age has nothing to do with it, fear is the factor in this situation if they are not trained and in her case, off course, at her age she is not. She is outside now, having eaten walking the gardens..
They have a fear of falling how big is the bed? How high off the ground?
Another reason is pain when urinating, you should check that out with the vets that there isn't a problem there, as they will just seek the comfort of going right there.. I thought that may be the problem with mine but I was assured it was old age and possibly hard for her to get off the bed, she had a stroke a year or so back so doesn't have full capacity of her back legs.
The other thing is jealousy, if you have a baby? They can smell the scent and will do the same thing in protection.
Another is instinct if there is another "new" animal in the house to mark his/her territory.
One more thing because he/she is a bubs, put a clock next to her/him so she/he can hear the ticking of the clock like his/her Mother's heart beat. Sometimes it can also just be pure fear of not feeling safe..