This will take 120-150 hours for most players. This is about 250 games of Conquest. There's not a whole lot you can do to speed it up. To the extent you can, here's what you should do:
- Play on double XP weekends.
- Get the First Win of the Day bonus on every playlist every day. You get extra XP for doing this and it'll speed things up considerably if you do.
- NEVER leave a game. If you leave games often, you get less XP (well, actually, you get extra for not leaving them)
- Buy XP boosters from the in-game marketplace
I'll note that while performance in the game does help, the main factor in XP game is time. As long as you're playing, you'll be gaining decent amounts of XP. So while it looks like Conquest gives more XP than Arena, that's really only because the games last longer. Basically, it doesn't matter what you play. You just need to play.