I want to buy a new bike and start riding again (I haven't ridden a bike since I was little but I loved it) and maybe lose a few kilos, but will my legs become bulky if I start riding regularly? I don't want them to.
Don't worry about it. Building lots of "muscle bulk" takes a lot of work over a very long time. Also, this happens to women a lot less than men. To see what I mean, go to a cycling event like a 100 mile ride and look at the women there. I think you'd like to look like them. Most are lean but toned.
Forget about your house of cards, And I'll do mine. You're muscles get bigger and start to define themselves, but your bones and the actual size of your legs stay the same. Cycling will just add shape to them, and greatly increase the size of your thigh muscles.
It's gonna depend on you tendency to add muscle. They will tone almost immediately, which shouldn't look incredible hulkish, but you shouldn't add too much muscle unless you train specifically to do that.
Just keep a high cadence and have fun.