If by bike you mean bicycle I can kind of advice against it since there was cases of crashes with bicycle foreign tourists in my region. Mostly from not very smart ones from japan and korea who decided to go in time of polar night if I remember correctly but still - old soviet roads across rocky hills is far from facy autoban and contain a lot ups and downs, dangerous turns. Road to Rovaniemmi espessialy from Kola following Tuloma river up to western side of Murmashi I can note as pretty dangerous one and there even currently some big constructions happening for some years with destruction of big parts of rocks so it is dangerous mess.
If you want it like motocycle, then well it's okay, Finnish bikers with scary fat faces I seen was pretty happy about that :---DDDD
I also should point out that distances here is not mongolia-syberia tier, but huge between cities and locations, not even in Murmansk region, but in central-northen karelia you may find yourself in middle of forest in hundred of kilomiters without gas station or town on main road. Same goes for road from finland thought like Alakurtti it's most probably crap. And if you follow road to rovaniemi back - there will be no tundra, it's just your typical Finnish pine forest. I can kind of advise to go from Rovaniemi to murmansk and then from murmans to Kirkines, Norway. Maybe with visit of Teriberka - there all your cool tundras, waterfalls, etc.
It's on norvegian road also where diferent alleys and war memorials, with some remained german bunkers somewhere if you interested in all this stuff.
Thought, moutians and parks with Saami, reindeers, huskeys is in central part of peninsula but it's better go to city and go for tourist agency there for a tour here than go by 70km from main road to lovozero in town itself and found out that it's shitty post-soviet dying city lol.