You won't burn any bridges. When people start looking around for options, this is not uncommon to happen.
If you ever go back to the company (which rarely happens) or for the same boss in a different company (also rare), you'll be considered for your merits and this incident won't matter. Go ahead and take the best offer you can get.
Also, don't ask your current employer to simply match the new offer. Ask 10% over that and see what happens. You have nothing to lose.