So I never dropped to bronze 5 but I did carry myself out of bronze 4 in season 5 and I carried myself out of bronze 3 this season (and still climbing.) I'll be honest, it's really freaking hard to carry in bronze as a support. I tried it and after about 10 games I was like "screw this." It's definitely possible because I've seen others do it but in my opinion support is the hardest role to get out of bronze with.
You really can only depend on yourself in bronze so it helps if you play champions that can solo carry the game. This is part of the reason why I shifted to ADC this season because I feel like it's currently the most important role in the game (all I did was jungle in season 5.)
However, you shouldn't play a role you don't enjoy just to try and improve you rank. Since you say you like volibear maybe you should try playing him in top lane or the jungle (in normals first.) After that maybe more onto some other tanky champs like Maokai and Nautilus. You only need like 3-5 champions that you can flex to 2 different roles in order to climb in ranked.
So I guess the real question is what do you want play?
General tips
- You should be looking to get at least 5 cs/min when top, mid or ADC.
- Never risk dying for a CS.
- If a tower is going to die don't stick around and die with it. Just back off and pressure other objectives.
- Towers are far more important than kills.
- One kill for one death is almost always not worth. You should be looking to average a KDA of at least 3 and also have at least 50% kill participation.
- Track cool downs like flash, teleport, enemy ultimates, and even their basic abilities. If all of an enemy's abilities are on cooldown or he doesn't have mana then you should look to try and trade with them.
- Wards save lives.