Hi Stereotype! I'm a bow maker, and I'm Swedish. Yay! Google my name, Nils Markus Nyström, and you'll find my website.
I live in Uppsala, a bit south from you. My guess is that your best bet for a self bow is rowan (rönn). Make sure it's straight grained though. Depending on how far north you are you could maybe find maple and bird cherry (hägg). Maybe even Swedish whitebeam (oxel) but I doubt it. Then, of course, you got all the garden stuff, cherry, apple, plum, etc. I've tried making a number of birch bows but have never had any luck. Some of my most frustrating bow making moments have been with birch. Just last week I had a birch backed bow develop splinters out of nowhere. Birch hates me. Of course it grows everywhere and dries easily, so it's an easy wood to come by. I suspect you should try to find birch that grows as dryly as possible. Give it a go and make the bow longer and wider than you want, maybe you'll be more lucky. If you ever pass through Uppsala, I can set you up with staves from hazel, elm, ash, maple. Just email me.