The best way to connect is a function of the total amperage draw of the floor mat, which you did not mention. The electric radiant floor heat in my kitchen uses approximately 12 watts per square foot, which is pretty typical. For a 100 square foot installation, that would require 1200 watts, which is about 10 amps at 120 volts (some mats can be purchased at 240 volts).
The problem with piggybacking off an existing circuit is that the mats draw continuously, so if you have a 10 amp draw, and you turn on a 12 amp hairdryer, you are going to blow the breaker on a 15 amp circuit, and possibly blow even a 20 amp circuit. If you are going to use a small draw mat, say 5 amps, you may be able to piggyback it on to an existing circuit.
The problem with piggybacking off an existing circuit is that the mats draw continuously, so if you have a 10 amp draw, and you turn on a 12 amp hairdryer, you are going to blow the breaker on a 15 amp circuit, and possibly blow even a 20 amp circuit. If you are going to use a small draw mat, say 5 amps, you may be able to piggyback it on to an existing circuit.