Jagged edges on Alpha to Select

[EDD]

I am getting jagged edges when I add an outline to text using the following method.

1. Type text

2. Layer > Transparency > Alpha to Selection

3. Select > Grow (3 pt)

4. Layer > New (Transparency)

5. Fill Selection using Bucket Fill Tool

6. Arrange layers so that the new layer is beneath the original text layer

The problem arises in Step 5 when the selection is filled.  The filled selection has jagged edges. How do I prevent these jagged edges?