It looks like you are dealing with font families and styling. Some receiving domains adjust the font to what it can read. Sometimes that includes not bolding text. Outlook is one system that likes to adjust font styling. Something to remember for Outlook that should help: Link first, bold second.
Outlook will often ignore the bold tag if it's outside the link, like this:
That will help in Outlook. For other systems, it should show up as you have it in the mailing.
A quick general reminder about fonts:
Fonts available in our editor: Andale Mono, Arial, Arial Black, Arial Narrow, Book Antiqua, Century Gothic, Comic Sans MS, Courier New, Georgia, Helvetica, Impact, Palatino, Tahoma, Times New Roman, Trebuchet MS, and Verdana.
Of those, fonts installed on iOS: Arial, Courier New, Georgia, Helvetica, Palatino, Times New Roman, Trebuchet MS, Verdana
If a contact views a mailing on their iPhone/iPad that includes an unsupported font, it's expected that the font would revert to something different.