Depends on which boss and what you do.
First thing ide do is get Piety. That would make yourself a lot more useful.
Bandos: 3 Options really
a) Solo
It's usually only possible to find a solo world at night- Bandos is very popular nowadays. For solo, after getting Piety and equipping Max def bonus with Karil's top using a Godsword or whip+DFS/rune defender you'll manage 1-2 kills per trip. Focus on maxed range defence with some magic defence.
b) Solo Crash
My favorite, but you'll need to have Piety, Recover Special Potions, and Claws/AGS to be of ANY competition against those other guys that are like near maxed with CLS+Overload+Turmoil..
What you do is you find a non-lootshare world that has like two people already in there, and you go in and try to steal their kills, drinking Restore Special potions in order to spam special attacks to steal their kills.
c) team
Different teams have different requirements, but ide get Piety first before you do anything.
Zamorak Boss:
a) Solo
Wear karil top+skirt, dragonfire shield, verac's helm, dragon boots, fury, ring of life, barrow gloves, zamorak cape, whip... Or use AGS in place of whip+shield.. shouldn't be hard to find an empty non-lootshare world. Eat always above 60HP, 70 to be safe. You'll manage one kill usually.
b) Team
Same thing really, but get piety first or no team will want you.
Armadyl Boss:
Unless you have 90+ defence, 68+ summoning, and armadyl top+legs, I'm pretty sure no team will want you.