The bill thing is allegedly to establish which legislative district (Congress, state, county and city representative and councilman districts) the voter resides in on voting day. Many poor people live in apartments and even small houses where the landlords hold the utility accounts and include it in rent, since many poor people have bad credit and can't afford the large security deposits necessary to start a utility account of their own. If the impoverished voter has no other regular bill, say for a credit card, and has no bank account statement - again, something not everyone can get if they have bounced checks in the past - they can be SOL'ed out of their right to vote. The reason it is bullshit is because when you Register to vote, you fill out and sign forms providing the required information to the polling officials, and they send your voter ID card to you after they have verified you are who you say you are. The cards typically are simple with no photo, but they are the law of the land. Legislation adding further requirements at the polling places add a hurdle that is at best in a Constitutional grey area, especially if requiring more than a common second ID, such as a state driver license or state photo ID (which you get at the driver license bureaus).
The other more pervasive way to disenfranchise voters is the judicial system; you lose your right to vote when convicted of a felony, such as possession of a small amount of pot or cocaine in their various forms.