If it’s clear to me, you’re seeking the builder pattern.

Below is an implementation based on your provided code snippet:

class DialogService {
    private _title: string;
    private _message: string;
    private _okBtn: string;
    private _cancelBtn: string;
    private _confirm: string;
    private _cancel: string;

    constructor() {}

    public title(value: string): DialogService {
        this._title = value;
        return this;
    }

    public message(value: string): DialogService {
        this._message = value;
        return this;
    }

    public okBtn(value: string): DialogService {
        this._okBtn = value;
        return this;
    }

    public cancelBtn(value: string): DialogService {
        this._cancelBtn = value;
        return this;
    }

    public confirm(value: () => {}): DialogService {
        this._confirm = value;
        return this;
    }

    public cancel(value: () => {}): DialogService {
        this._cancel = value;
        return this;
    }

    public show(): void {
        bootbox.dialog({
            title: this._title,
            message: this._message,
            buttons: {
                cancel: {
                    label: this._cancelBtn,
                    className: 'btn-inverse btn-inverse-primary',
                    callback: this._cancel
                },
                okay: {
                    label: okBtn,
                    className: 'btn-inverse btn-inverse-primary',
                    callback: this._confirm
                }
            }
        });
    }
}

Following that:

new DialogService()
    .title('Some title')
    .message('Some message')
    .okBtn('Sounds Good')
    .cancelBtn('No way!')
    .confirm(() => {})
    .cancel(() => {})
    .show();

Edit

I observed the modified question after my initial edit, so I am re-editing it:

interface ButtonData {
    label: string;
    className: string;
    callback: () => void;
}

class DialogService {
    private static BUTTON_CLASS_NAME = "btn-inverse btn-inverse-primary";

    private _title: string;
    private _message: string;
    private _okay: ButtonData;
    private _cancel: ButtonData;

    constructor() {}

    public title(value: string): DialogService {
        this._title = value;
        return this;
    }

    public message(value: string): DialogService {
        this._message = value;
        return this;
    }

    public okay(label: string, callback?: () => void): DialogService {
        this._okay = {
            label: label,
            className: DialogService.BUTTON_CLASS_NAME,
            callback: callback || function() {}
        };

        return this;
    }

    public cancel(label: string, callback?: () => void): DialogService {
        this._cancel = {
            label: label,
            className: DialogService.BUTTON_CLASS_NAME,
            callback: callback || function() {}
        };

        return this;
    }

    public alert(): void {
        bootbox.dialog({
            title: this._title,
            message: this._message,
            buttons: {
                okay: this.okay
            }
        });
    }

    public confirm(): void {
        bootbox.dialog({
            title: this._title,
            message: this._message,
            buttons: {
                cancel: this._cancel,
                okay: this.okay
            }
        });
    }
}

older edit

I’m still unsure about your specific requirements. I made some adjustments and included both `confirm` and `alert` methods, though their functionalities are not entirely clear...
The `confirm` method utilizes the existing `bootbox.dialog` from your code, but for the `alert`, I improvised with a `bootbox.alert` function.
This may not be accurate, so you might need to implement it as needed...

interface ButtonData {
    label: string;
    className: string;
    callback: () => void;
}

interface ServiceData {
    title: string;
    message: string;
    buttons: {
        cancel: ButtonData,
        okay: ButtonData
    };
}

class DialogService {
    private static BUTTON_CLASS_NAME = "btn-inverse btn-inverse-primary";
    private data: ServiceData

    constructor() {
        this.data = <ServiceData> {
            buttons: {
                cancel: <ButtonData> {},
                okay: <ButtonData> {}
            }
        };
    }

    public title(value: string): DialogService {
        this.data.title = value;
        return this;
    }

    public message(value: string): DialogService {
        this.data.message = value;
        return this;
    }

    public okay(label: string, callback?: () => void): DialogService {
        this.data.buttons.okay = {
            label: label,
            className: DialogService.BUTTON_CLASS_NAME,
            callback: callback || function() {}
        }

        return this;
    }

    public cancel(label: string, callback?: () => void): DialogService {
        this.data.buttons.cancel = {
            label: label,
            className: DialogService.BUTTON_CLASS_NAME,
            callback: callback || function() {}
        }

        return this;
    }

    public confirm(): void {
        bootbox.dialog(this.data);
    }

    public alert(): void {
        bootbox.alert(this.data);
    }
}