Is a bed considered pure or impure if it is highly likely that urine has stained it under the outer covering, and how can it be purified if it is difficult to determine the exact spot of the impurity or to wash it?

The method for purifying bedding if impurities have reached its inner layers is found in Fatwa (definition) no. 116814. If you doubt whether impurities have reached the inner layers of the bedding, the basic principle is that they have not, and it is judged to be pure, because the transfer of impurity is not established by mere doubt. If you are unsure about the contaminated spot, you should investigate and wash the part that gives you certainty or a strong presumption of its purity.