Is there an algorithm to bold an outline font?

The best way to do proper outlines, is unfortunately, also the hardest. It involves calculating an offset curve, usually from the medial axis or straight skeletons, which are non-trivial to calculate. Once you have those, you can calculate the distance of any point from the input object and decide whether to draw the outline or bolding, or not.

A simpler way to do it, which doesn't look quite as nice, is to use a MinMax filter. This is a sliding 2D box filter that calculates either the minimum or maximum value within the box at each input pixel. If you have black text on a white background, you can use the min filter to generate an outline. Use the max if it's white text on a black background. Other shapes, such as a circular area will produce different results that may be better for some fonts. In most cases, you'll end up either rounding off or squaring off corners as the size of the filter increases.

I think dilation would be close enough to what you want.

It is likely that font processing software would have more advanced algorithms to avoid rounding all the corners, among other things. Fonts are a whole separate world with a lot of rules about how things should be done to look right. No simple image processing algorithm will respect all those rules.