TLDR; specific practice listed in last paragraph, justification for why that will work is above
So I'd say lolking.net or na.op.gg the people you're playing with in ranked and check their rank. If you were demoted silver to bronze (or gold to silver etc) then at least the way rito said it was that you have to have MMR a full tier below your rank, so you may be playing w/ people like bronze IV and bronze V. I had the issue of doing okay in normals and being crushed in ranked when I first started and part of that is probably the same issue I had; low nomals mmr. Look up the summoners you play against in normals and I bet most are unranked or bronze, so you have an easier time in normals than ranked. That was my issue at least.
In bronze a lot of it can come down to practicing the basics. silver III or so is the 50% mark for accounts if I remember right, which means below that is a little less than average rank, and above that is slightly better than average rank. If you're playing mid to low bronze players then it should be well below average ladder rank, and you can have a big influence on the game just by improving to average or slightly above average on the basics. For instance I played a TON of heimer this season and made it to gold, but start losing lane w/ him to players in the gold III to gold I range, so my Heimer skills are decent but not great. I played him in some bronze games (my normals mmr is probably still bronze and definitely was until I played some normals this season, and I had a second account from leveling w/ my friend) and absolutely crushed most games bc people don't judge damage well in bronze and so I could usually tower dive for a kill at level 6 and would be up 15-20 cs plus a kill after first or second buy and so my advantage was huge from there bc I just kept pushing it.
Things to practice:
-CSing; no one can cs in bronze, try to average 60-70 cs at 10 minutes, it's not great but it will be FAR better than anyone in bronze and will probably add up to a kill or kill and a half in terms of gold advantage from CS. Practice in customs if you need to, or just try to improve in ranked if you don't like customs (like focus primarily on cs for the first 10 minutes of a few games and see how high you can get w/out giving up a kill to your enemy)
-Judging damage and trading; People don't judge damage well in bronze, if you take half your HP in burst from a champ, don't stay in lane at 25% hp w/ no pots to heal up. Similarly, notice if an opponent is fighting you and doing = damage but you have more sustain (pots, life steal, a heal in your kit, whatever), or if they are consistently taking more damage when you fight and don't have more sustain. If either of these is true, fight when you can, it will push them out of lane or get you a kill. Often learning this takes time.
-Learn to control minion waves; you should know how to freeze a wave just out side your tower, so if you can freeze and they can't push enough to break it the enemy has to come up more in lane to cs; this makes them easy to gank. Also you should know whether your minions will hit their tower or not after you get a kill/jungle ganks and forces them back. If you can you always want to shove the lane to tower when they are dead or leave, because they will lose cs and exp to the tower killing minions faster. Search Youtube for a channel called "how to top lane" for a good explanation of how to do this.
-Learn to use your mini map; Don't just ward, actually notice when someone is walking over your ward. If you ward enemy jg or take scuttle and you see their jg ping it for players not looking. I'm shit at this, but try to look at your mini map every 5-7 seconds w/out letting your lane play getting worse. It's hard to do, and I forget this a whole lot, but you'd be amazed how much it helps. You'll notice the support leave bot lane and maybe check dragon or play a little safer mid lane and suddenly you can contest drag instead of giving it for free, or not have a death bc you got ganked. You'll notice the enemy jg go into your jg and ping to collapse and suddenly you have a kill you would normally not get, plus their jg is behind instead of yours.