If you have a welder then use it to weld a nut onto what is left of the bolt shaft. This method will more or less guarantee to save you the bother you'll inevitably get trying to drill out the bolt.

Failing that, as mentioned - you'll have to drill it out.

The reason why your drill bits are becoming blunt very quickly is because you are probably using an incorrect surface speed for the diameter of the drill bit and rotating them at the incorrect speed; larger diameter drill bits need to be rotated far slower than smaller ones. High RPMs with larger diamter drill bits causes excessive heat, its the heat which dulls the bit quickly.

If I were you I'd consider not only using the correct RPM but also using oil to both cool and lubricate the cutting edge of the drill bit.