Formal: Queen Elizabeth the first. / Queen Elizabeth the first of England.
Slightly less formal: Elizabeth the first. If the context is clear you can say Queen Elizabeth or just Elizabeth.
Informal: Queen Bess, Good Queen Bess (not that I think she was particularly good). Horrible Histories call her Liz the First and Good Queen Bess (see link below) Also they say Queen Liz Two for Elizabeth II. Things like "Liz one" and "Liz two" would be okay in an informal context when it's clear you're talking about monarchs.
Yes, this entire post was an excuse to post a link to the Horrible Histories monarch song which is great fun.
If someone is literally reading "Elizabeth I" then you could read that as Elizabeth one or Elizabeth the first, the latter being the safer bet in academic circles.
ETA: it's not letting me post the link without turning it into an embedded video
Let me try this way.
ETA#2: it worked