This is a good opportunity to re-frame your value to the company. Instead of focusing on hours worked, focus on what value you are bringing to them. If their website is a core part of their business, it's enormous - they're getting the peace of mind that if anything happens they have someone reliable they can call to get things fixed. Depending on the company, you might even be able to figure out exactly what 2 hours downtime means to them in $ terms and go from there.
You should look into Jonathan Stark [1], he talks a lot about "hourly billing is nuts" and how to think differently about how you work/think about your time. For example:
https://jonathanstark.com/how-i-realized-that-hourly-billing...