You're gonna want to stick with real people if you're looking to learn the game. Friends are ideal, if they're at your skill level. Bots are for getting familiar with the UI or if you want to experiment with a hero you've never played before. Try not to depend on them for learning how the game works... mechanically.
Bots are kinda restricted to a certain playstyle, and anyone who plays with them enough learns the best way to beat them is brute force via massive farm, which is a TERRIBLE way to play against actual people. Hence all the Mortreds and Ursas and Phantom lancers and Nightstalkers roaming about in lower pools, because supports and nukers lose out their effectiveness pretty fast there.
And don't be so nervous about how you play! Everyone sucks when they start out. And the learning curve for these kind of games is like, STEEP. It takes everyone a couple of months before they've got kind of a comfort zone in how and what they want to play. Until then, just realize you don't need to be the team's doormat, and chat ignore functions exist for a reason. The vocal side of the community can get pretty loud and obnoxious, but there's plenty of friendly people about as well who're just there to learn and have fun like you.
I've got a friend who kind of 'plays by himself' and 'tries not to get in anyone's way' and so far it's done nothing but worsen his self esteem. You don't improve too much unless you're willing to take risks, and it's only when you fail a bunch of times do you find that one glorious moment where you pull off something AWESOME and INCREDIBLE and it makes all of those past failures TOTALLY worth it.
This might sound like afterschool special territory, but it wouldn't hurt to try making friends with some of the people you play. I guarantee you Dota2 and LoL both become a billion times better when you've got someone to rely and depend on when the assholes come out to pasture. It opens up a bunch of options to you in terms of lane combo's and such as well, plus you can patch up holes in your team better without thinking 'oh hell, oh hell, they all just picked 4 melee carries'.
So yeah, best of luck with your future endeavors. You'll umm, need quite a bit patience too, so I hope you have that.
Edit: Just remembered something. I'm not sure how League works since I didn't really play it long enough, but DotA2 very frequently shakes things up with rebalancing of heroes, sometimes overhauling entire abilities or heroes in the process. I'd suggest you stay updated with the patches. Someone above suggested the Wiki, which is a good idea imo, since otherwise you'd never know for instance that Meepo has an innate 35% resistance to spells, as opposed to the normal 25% that every other hero has.
Umm, oh right, if you don't know already, every single hero in the game takes 25% reduced damage from spells. If they're of the magical variety. There's certain spells that are modified by armor as well (like Leshrac's Diabolic Edict), and others which ignore all kinds of resistance (like Tinker's Laser).
This might come in handy if you're relying on a hero's spell for the final kill, like with Sniper's assassinate, Lina's laguna blade, Lion's finger of death. It's handy to remember the 'actual HP lost' instead of looking at the raw damage, so you don't end up missing a kill. This comes with natural guesstimation later, but remembering Sniper's assassinate always kills at 266 hp or below (when it's at level 6) has been very, very useful in my early days.