Use 'stumble across' when you find something unexpectedly while doing something else. She stumbled across an old love letter while she was redecorating her room.
Pro Tip 2/3
Chance Encounter
'Stumble across' suggests a chance meeting of people or animals unexpectedly. I stumbled across my old teacher while hiking in the mountains.
Pro Tip 3/3
No Active Search
'Stumble across' implies that there is no active searching involved; the discovery is made by luck. On my walk, I stumbled across a rare bird nesting in the bushes.