Как я могу создать интерфейс в VB.NET с неявными реализациями

No, System.Windows.Forms.Form doesn't have the FormInterface implemented, so VB.NET doesn't know they match. VB.NET doesn't do implicit interface implementation, just explicit.

Yes, you should create a base class and implement your interface on that. I would, however, name them slightly different. Perhaps DoShow and DoHide.

Something like this:

Public Class BaseForm
    Inherits System.Windows.Forms.Form
    Implements FormInterface

    Public Sub SetupForm() Implements FormInterface.SetupForm

    End Sub

    Public Sub DoShow() Implements FormInterface.DoSHow
        Me.Show()
    End Sub

    Public Sub DoHide() Implements FormInterface.DoHide
        Me.Hide()
    End Sub

End Class

Else you could by accident do this:

  Public Class BaseForm
    Inherits System.Windows.Forms.Form
    Implements FormInterface

    Public Sub SetupForm() Implements FormInterface.SetupForm

    End Sub

    Public Sub Show() Implements FormInterface.SHow
        Me.Show()
    End Sub

    Public Sub Hide() Implements FormInterface.Hide
        Me.Hide()
    End Sub

End Class

And that will crash and burn.

Don't make the baseclass MustInherit, because the forms designer won't like that.

Unless you intended to use protected members of the Form class in Form1 members, I would use a containment relationship instead of inheritance. So you would have your FormInterface named something like IFormWrapper instead, and your implementation would be like this (I show it in C# because it is my working language, I think you will be able to translate the idea to VB):

public class Form1 : IFormWrapper
{
    private readonly Form form;

    public Form1 {
        this.form=new Form();
    }

    public void Show() {
        form.Show();
    }

    public void Hide() {
        form.Hide();
    }

    public void SetupForm() {
        //Code for the setup method
    }
}

After all, if you were planning to use Form1 instances through the FormInterface class, you would have had no access to the Form members other than Show and Hide.