There aren't very many ways to increase base attack bonus even temporarily, and only one I know of that would increase it permanently, other than leveling up. The spells Divine Power and Tenser's Transformation can increase it temporarily. So will a level-10 War Chanter (with at least one ally who already has BAB 20). But neither of those would help with meeting the prerequisite for the prestige class. (There are some other ways of bumping up a low BAB, like a Skillful Weapon, but those would only get you to 0.75 BAB).

The only permanent way I know of doing it would be to contract lycanthropy. Becoming a lycanthrope adds the were-critter's BAB to yours. Unfortunately if you're aiming for Elemental Master, you need to be a Dragon, and Dragon isn't a valid target for lycanthropy.