Can acid reflux cause tongue to burn and bumps to form on the base?

Doubtful: I've never heard of this happening. While i suppose it's possible, i doubt this is what's causing your burning tongue.

Possibly: Acid reflex has many oral ramifications. Your tongue burning can be a result of the irritation to the surface and papillae(taste buds). They can swell or overgrow, change colors, become painful, etc. It cause dental caries and breakdown of fillings. Your susceptiblity to cancer is higher, too. Check it out with your dentist.