Mattresses are a nightmare and it is difficult to get any kind of decent result on them. This is due to the composition of both the face material and the stuffing.
The staining is usually body fluids, sweat, urine etc.
You are best off using an acid based product such as cotton cleaner as the staining will be acid rather than alkaline. Reducing agents such as spray n Go can reduce the stains as well.
Beware of over wetting as I have seen severe rust stains where the operator has over wet and caused moisture to come into contact with the interior springs.
Best to dry off with an airmover before you leave.
Pre-vaccing with a good vacuum cleaner or Hunter vac will remove a lot of the loose debris prior to wet cleaning.