Your battle styles for your Ledian and Ariados should be switched, haha. :P
This may be an amusing moveset (Like a real spider: trap the victim, then slowly wear it away to nothing. So cruel, yet hilarious!), but Ariados does not have the bulk to trap an opponent and whittle away its HP little by little, when you could just sweep the opponent with a strong attack. Ariados just doesn't have the survivability to utilize Toxic and wait it out, along with the other unnecessary tactical moves.
If anything, you'd want to keep toxic to make the opponent switch out, not be trapped and forced to attack a defensively average fighter like Ariados. Keep Toxic if you want to, but I'd replace it with a Poison-type STAB, like Poison Jab.
Spider Web? Forget about it. It's a great tactical move, but the only Pokemon that can learn it just don't have the bulk to trap the opponent and make them scared of not surviving. Replace it with Psychic, so you can hit other Poison-types, hit Pokemon that resist your other attacks, and to pick off Fighting-types with ease.
And Agility should be dumped too. Even with 40 Base Speed and maxed Speed from agility, you're still not going to outrun many threats. Replace it with Shadow Sneak, so you can revenge kill, and not have to worry about that terrible Speed Stat.
Bug Bite, like you said, compliments Attack, STAB, blah, blah, blah, etc. etc. You know what you're talking about.
All in all, you have a good strategy, but Ariados isn't about strategy. If Ariados had some kind of reliable recovery move or more general bulk, then that would be a great moveset, but due to Ariados' mediocre Defenses and HP, it just doesn't work on him. Go for a more straightforward, offensive approach.