I have some "Mustang" oiled leather from Tandy purchased about three years ago now. Made this bag, a guitar strap and a belt.
It is lovely stuff and has not bled out, though I do heed warnings and store oiled leathers away from all others. Some oiled leathers will bleed more than others. For example, my prized Horween leathers get their own shelf space as they have a bleed out potential and are my precious. If you have seen a really old piece of leather, like say a veg tan baseball glove, it can dry out after long time and that when it needs to be re-fed.
Keep your oil tanned rolled, covered and out of sunlight. If you think it has dried out, just re feed it with whatever oil based product is available to you...there are lots!!
Tandy takes such a bad rap one here, but if you are careful in selection, go to the store, feel/pick the leather yourself and buy stuff on sale you can do just fine!!