It can't be that hard, yeah? Over time I'll stop hitting multiple strings?

If you mean by "single plucking"; that you want to pick a single string, but instead you're hitting multiple strings, then sure.

Though, picking a single string shouldn't be all that difficult. I imagine you're trying too hard if you're having a rough time of it.

Best tip I can give to newer players (and anyone really) is to just ease up. Use the least amount of effort and pressure as possible.

You may also want to adjust the angle of your attack on the strings for even easier picking.

2 hours ago, Menaxe said:

 Over time I'll stop hitting multiple strings?

Yes, but it doesn't mean it just corrects itself. 

It's hard to tell without seeing you play, but if you're still a beginner on the guitar (because this is usually a guitar problem, not bass, and it's related to using the pick) then maybe it's possible you are swinging the pick too much. Many people when they start on an instrument, they instinctively think it's gonna be hard and therefore that they have to hit it hard, but that's unnecessary even with drums, much less with an amplified guitar.

If I were your teacher, I would check that when playing lead parts you're not doing the same wide right hand movements as when you're strumming: you only need a very minimum movement of the wrist to play single strings. I would also check that you're not slamming down on the strings from far away, again you only need to activate a string's vibration with a small pressure, not hitting it like a hammer hits a nail. It is also possible that you're dipping the pick too far below the string, while you only need a millimetre or so of the tip of the pick to hit the string. Last but not least, you are using both downstrokes and upstrokes, right? Because if you only use downstrokes then it's going to be twice as hard to control your pick and to decrease efforts. 

It's definitely achievable with practice! Focus on developing a controlled and precise picking technique. Start slow, using exercises that isolate single-string plucking. Gradually increase speed as you gain confidence. Also, try muting the strings you're not playing with your left hand or palm.