It's not a good idea to use bindings in your case and there is no "easy" way to make it because bindings is one-to-one relationship.
If you want use bindings you should make one property in your model with 3 options:
typedef enum {
OptionValueA,
OptionValueB,
OptionValueBoth,
} OptionValueType;
@interface Model : ...
...
@property (assign) OptionValueType optionValue;
...
@end
And also could optionally use a value transformer to bind it to your button.