I don't think it's the job of the solicitor to go chasing utility bills. It's nothing to do with title. Different matter for bills that run with the property, ie rates, NPPR, local property tax etc.
The OP is not liable for the bill, but they could help the rest of us in keeping electrcity costs down by suppling the ESB with the address and phone number of the previous owner. I've done this when my tenant's leave and ESB cannot find them. People not paying their bills only creates hassle for honest payers. In this case it might just be an oversight.