Double XP weekends are obviously a good way to get this done, as is playing on insane as you get more XP for higher difficulties. I find that playing on lower difficulties attracts players that are prone to being unskilled and others that will drop immediately. This happens quite frequently on casual and normal.
For me at least, playing on insane provided a decent group of players, that more often than not, were serious about getting to level 50.
You will need to play though on insane roughly 3 times to get the required XP (twice on double XP weekends) Don't forget to buy packs between each run, level up and assign class cards to your chosen class.
Personally I did this as a heavy and as I went through I equipped cards such as:
Marked Dmg: to give your team mates the best opportunity to help you through, don't forget to spot enemies
Explosive Capacity: gives you more boomshot rounds/capacity on spawn and will give you extra salvo capacity etc as you scavange explosive weapons
Explosive Dmg: Make better useof those explosive rounds
Heavy Wpn Dmg: More damage for weapons such as the mulcher, tri-shot, buzzkill etc