How to play Halo 4 against bots

Based on my own service record and what I remember of the few times that I played Flood, the "Other" weapon is the map itself. So falling to your death without getting shot, and I'm not sure what else would.

Personal Ordnance drops are obtained in Infinity Slayer and Big Team Infinity Slayer.

As 343 explains it:

As you earn medals, you fill up your ordnance meter. When that meter is full, you earn a reward drop for yourself from the Infinity. The reward comes in the form of three randomized power weapons, grenades, or powerups (two of the former, one of the latter). You can then choose which one you want, and the Infinity will drop the ordnance (if you’re inside, it will teleport in). You won’t get the highest tier power weapons (e.g., rockets) in personal ordnance, but everything you do get is powerfully awesome. And awesomely powerful. And everything in between.

The key part being "As you earn medals". Therefore the ordnance meter fills faster for doing more 'stylized' kills, such as Multi Kills, Assassinations, Retributions, Reload This, and the many more medals.

For an example:
If you throw a plasma grenade that sticks to an opponent who was reloading, then quickly assassinate another opponent, all while being shot at and then your team-mate kills the opponent shooting at you, that would net you 5 medals (Plasma Kill, Reload This, Assassination, Double Kill, Distraction) and significantly increase your ordnance meter.

Also a note from my own experience, you cannot receive an ordnance drop while in a vehicle. The meter still increases for what you do in said vehicle, but it will not show you how full the meter is nor will it inform you if it is full until you jump out of the vehicle, or you die. If you happen to die in the vehicle, or whenever you achieve an ordnance drop, you will retain the earned drop and be able to call it in when you next spawn.

Check out tombull89's answer below if you want to see point totals required for each drop.