Can I refuse entry and/or service at my retail business (food service, grocery, book store, etc.) to individuals wearing face coverings? i'm specifically interested in religious coverings such as hijab/niqab/burka. If individuals ignore this policy, would it be trespass and would that mean I could call the cops to have said individuals removed?
You do not give a jurisdiction so I will assume Australia.
Discrimination is legal unless it is for a prohibited reason
One of the prohibited reasons is if it is on the basis of a person's religious beliefs.
So, you are completely within your rights to an individual wearing a face covering provided that the wearing of such a covering is not part of that person's religious belief.
So, you can say no to motorcycle helmets, baseball caps and balaclavas - you cannot say no to a hajib if it is worn as a religious observance of either Islam or Christianity, a habit if worn by a Christian nun or a kippah worn by an orthodox Jew. Providing your policy contains such exceptions you are good to go.
You can refuse entry to or eject anyone. The police might point out that you are likely to get sued, and there might even be a local ordinance that would prohibit them from enforcing a property-owner's trespass complaint if it appeared discriminatory. You would be in violation of Title II of the Civil Rights Act of 1964, via 42 USC 2000a, so there would be consequences.
All persons shall be entitled to the full and equal enjoyment of the goods, services, facilities, privileges, advantages, and accommodations of any place of public accommodation, as defined in this section, without discrimination or segregation on the ground of race, color, religion, or national origin
A complaint could be lodged with the Department of Justice, or the party could file suit directly. There are also state regulations against this (Washington: RCW 49.60.030), and in Seattle and some other places, city ordinances.
Even if you spin the restriction as simply about face covering, under a "disparate impact" analysis, this would almost certainly be found to be religious discrimination since it would predominantly affect Muslims.