Should Mom's Knife or Brimstone be found in a devil room, do not pick it up as it will create no effect.
Butt Bombs are more valuable than The Bean as a weapon since one bomb can confuse and slightly damage every enemy in the room while dealing high damage to any enemies caught in the blast. This is especially important when enemies can not be reached to damage directly.
Buying bombs in Shops is important. However, buying Bogo Bombs or the Humbling Bundle will provide higher returns in the long run.
The 2 of Clubs card is an extremely valuable resource as it allows a far more liberal placement of bombs. A bomb count of 49-50 will get the most out of the card's effect.
The Bombs are Key pill will be a major problem for the duration of the challenge. It is possible to counter the effect by using the pill again, but it is advised not to rely on that.
It may also be effective to have Remote Detonator as it would allow Isaac to both concentrate multiple bombs to easily kill a boss and would also greatly reduce the chance of taking damage from a stray bomb.
If running low on bombs, it may be wise to look for familiars, as they could help with some extra damage. Powerful familiars such as Incubus and Succubus can make the challenge much easier.
Safety Scissors are invaluable, as they will allow the player to restock on bombs by collecting defused Troll Bombs. Together with Curse of the Tower it will ensure the player will never find themselves without bombs, as long as they can afford to take damage, while the Anarchist Cookbook will give a quick and steady refill of bombs thanks to 9-Volt.
Getting Match Stick will increase the chance of finding bombs.
Getting an orbital such as Cube of Meat on the first floor can provide a more reliable source of damage than the starting items.
Anarchist Cookbook: Troll Bombs spawned retain Butt Bomb damage, and item recharges every other room. While The Bean's multiple uses per room are lost, conserving bombs become much easier as the book can wipe out most enemies in a single room in one shot.
Bob's Brain: Works basically as a free combat bomb every 10 seconds, with the bonus of having poison damage. Can be fired with the blindfold on, providing a decent ranged option apart from normal Butt Bombs.
Safety Scissors: Troll Bombs and Megatroll Bombs that spawn will be converted into regular Bombs, and in combination with the Anarchist Cookbook, can provide a nearly limitless supply of Bombs for the run.
Items that grant bombs such as Bomb Bag and Boom! can be useful to avoid running out of bombs.