I'm having trouble with the call-template element.

Here's how I'm using it in my stylesheet:

<!-- p template -->
<xsl:template match="p">
<xsl:text /><xsl:apply-templates /><xsl:text/>
</xsl:template>

<!-- bu template -->
<xsl:template match="bu">
- <xsl:call-template name="p" />
</xsl:template>

Yet if I call Xalan (1.3 on Linux), I get this error:

XSLT error: Could not find named template., style tree node:

What confuses me is how Xalan says it can't find the template when it's there.

That's because you confused named templates and templates
matching elements. You use
 <xsl:apply-templates select="p"/>
to tell the processor to apply tepleates to the elements
you have selected.
You use xsl:call-template for calling a named template, i.e.
one declared for example as
 <xsl:template name="p">
   ... stuff ...
 </xsl:template>

You can have both a match and a name on a template,
though this is a bit unconventional.

In your case, adding a name="p" to the template with
match='p' appears to do what you want, apart from:

> <xsl:template match="p">
> <xsl:text /><xsl:apply-templates /><xsl:text/>
> </xsl:template>

The <xsl:text/> are no-ops the way they are applied.
If you strip them, the template becomes:
 <xsl:template match="p">
   <xsl:apply-templates />
 </xsl:template>
Calling this after adding a name is the same as
using xsl:apply-templates in the ssame place where
you call it. Furthermore, the template does exactly
the same as the built-in template matching p, so you
can omit it completely.

Furthermore
>  Xalan (1.3 on Linux),
Upgrading to a more recent version is strongly recommended.
2.3.1 is available.