Im running a campaign with 5 players at lvl 3. One of them have been cursed with Lycanthropy from a werewolf bite and I have a bit of a problem with coming with an interesting way too allow the player to play around with it. 

I have had a talk with the player about the fact that he might try to kill the other PC´s and have him rolling wisdom saving throws to see if he losses control off his character over time. But I cant come up with a fun and interesting way for him to gain some control over the curse. I was thinking about doing a questline to find a druide who can help with this, but are looking for some inspiration.   

Silver and Wolf's Bane are common themes for Lycanthropy. Either could be used as a temporary patch. For example, you could let him wear an "Amulet of Discipline" which essentially gives him control over his new form, but also gives him a penalty, such as damage vulnerability or disadvantage on skill checks.

Long term, magic is probably the easiest mechanism. You could have them undergo a "Lunar Binding" ritual that seals the "aspect of the wolf" within him, but he could burn a spell slot or other class feature to draw it forth for some period of time.

There isn’t really anything to allow you to control the lycanthropy in place so you are free to come up with whatever you wish. You could seek out good lycanthrope or wearwolf communities and maybe they would have something to help. In forgotten realms you could look for the elven Lythari (a race of good wolf lycanthrope) or swanmays (induced swan lycanthrope)The Akri: a tribe of werecats who lived in the Anauroch desert. The Gray Wolf Tribe: a tribe of Uthgardt barbarians who were all werewolves. The Blood Screamers: weremole gnome bandits of southwest Faerûn and followers of Urdlen. 
You could find an ancient cure that changes their race to a shifter as a measure of control over the disease. or they could multiclass into barbarian as a way to control their lycanthropy and when they rage they become more beastial than normal as the werewolf tries to escape. 

Actually... you could do worse than having them multiclass into Path of the Beast Barbarian... I'd have them seek out some community of werewolves, as suggested above, but that would be a nice way to skin the cat, so to speak.

lycanthropes are not meant to be for player characters to be honest. its essentially a save or suck type of death. once he transforms that's it he is no longer himself until the transformation subsides. it shouldn't be you might try to bite them ; its you will try to bite them. the party needs to be sure they are willing deal with something like that because essentially 1 day every month he needs to be locked in an adamantine straight jacket coated in silver. that being said it should be a really big deal and i would expect the pc's to be concerned if not out right against traveling with an infected.

but that being said what i would do is inform him that he now has to use the shifter racial template instead of OR on top of (if you want to give him some sort of benefit ) his current race. but make sure they under stand that once a full moon hits he's going to lose control till the sunrise. the moon suddenly plays a big role like an ever present doom clock every night remind how it feels like. such as " you try to get some rest but even with an overact sky you can feel the waning moon slowly drifting through the sky. its haunting  song calling to you; you resist the urge inside to howl or scream. it wont be long now a few more days and you will not have that choice.".

as for how to end it its easy enough remove curse fix's the problem if he has not transformed yet (not sure about after). if he needs to deal with this the hard way their are nature spirits/gods of moons and animals or even fey if they get desperate that should be able to help. make it a quest but make sure that the moon is pressing them for time. if the party is in the middle of doing something important simply have the moon be at a phase that lets them deal with their current issue first.

I like the idea of finding some good lycanthropes, would fit in pretty nice with the setting I am doing. But the group (myself included) is all new players, so dont know if i wanna suggest multiclassing, plus the PC is a bard so not sure if the player is game on talking some lvls in barbarian. But i might just borrow the idea too find an ancient forgotten cure.  

and have been making it clear to the player that he has no control over his character when him transforms and that he might just get killed by the group if he does nothing about it. The other PC´s have no idea, that He is cursed, so the ball is pretty much in hes court as for the RP element of it. 

Depends on campaign. However the whole lycanthropy thing where they are immune to normal weapons is a pretty dangerous subtext. Which could be fair to say that if keeping it, resistance at best. While gaining the effect when they transform. 

Many movies have the werewolf tend to be a mental battle before they lose it. Such things as being hit or a side concentration ability since heightened blood pressure of combat can make it a thing that the benefits outweigh the negatives after a while. Especially if they are near where they have family, or don't want to bring harm to people. Nothing like having them rampage over a rest while they were in the inn, waking up in a barn covered in blood and guards on high alert because a nearby house looked like a rabid dog butchered a family. Just a slow start that "hey, this is a thing that happens with nothing I could do about it" then maybe if you got a plot hook that sends them further away, could have an npc mention some strange feeling of unease around them, or is also a lycanthrope who heard of a rumor, but needed mercenaries people don't care much about and offers what was snagged from a house they killed people in recently.

Maybe a old halfling by the lake makes a travelers stew that could ward off all ailments. (basically just an old lady making food for the youngsters and tell them stories. Since a sweet old lady and perhaps some guilt of a chance to wolf out and kill her would be a good thing to bring up. Call it an alignment check of sorts. Maybe that second serving that gave a belly ache had a bit of an effect. Either they want to not risk killing granny, or the party hopefully prevents it. Maybe the for mentioned wolfsbane could be an herb she used in the stew for flavor and a story she tells hints to a shrine of the moon. Oddly having wolves near it that howl on full moons.

There could be a means to offer the choice to remove it entirely, gain some control (like once a day for an hour can transform. But if under half health, you may attack anything closest to you. Such from order of the lycanthrope) Or embrace it. Which may be a larger change to class or race. Maybe they gain control but now wolf person or features. Maybe make that an option since why not in a world with lizard people, cat people, and even fish people? 

The granny could be a being in disguise. Such as a hag, or celestial, or fey. Just in case you want a little extra insurance on her not being killed or that the stew she makes is actually able to give a random blessing that lasts 48 hours and the bowl gives the effect of greater restoration. Just some ideas