I think Michael's suggestion to use xsl:number is the way you want to use as long as you want to number all <b>EXAMPLE</b> in any disp-quote, even a single one; if you only want to number them if there is more than one disp-quote in an adjacent group then the suggestion made in a comment might help:
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:xs="http://www.w3.org/2001/XMLSchema"
exclude-result-prefixes="#all"
version="3.0">
<xsl:mode on-no-match="shallow-copy"/>
<xsl:output indent="yes"/>
<xsl:template match="sec[disp-quote]">
<xsl:copy>
<xsl:for-each-group select="*" group-adjacent="boolean(self::disp-quote[p/bold = 'EXAMPLE'])">
<xsl:choose>
<xsl:when test="current-grouping-key() and tail(current-group())">
<xsl:apply-templates select="current-group()" mode="number-examples"/>
</xsl:when>
<xsl:otherwise>
<xsl:apply-templates select="current-group()"/>
</xsl:otherwise>
</xsl:choose>
</xsl:for-each-group>
</xsl:copy>
</xsl:template>
<xsl:template match="disp-quote" mode="number-examples">
<xsl:copy>
<xsl:apply-templates>
<xsl:with-param name="dq-pos" tunnel="yes" select="position()"/>
</xsl:apply-templates>
</xsl:copy>
</xsl:template>
<xsl:template match="disp-quote/p/bold[. = 'EXAMPLE']">
<xsl:param name="dq-pos" tunnel="yes" select="()"/>
<xsl:copy>
<xsl:value-of select="., $dq-pos"/>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>
Thanks for reply @Martin Honnen!
@Sandy, if the the reply solved your problem then you can indicate by accepting the answer, then it is clear the question is solved.