This sounds like it could be Heir Apparent (2002) by Vivian Vande Velde.
In the virtual reality game Heir Apparent, there are way too many ways to get killed--and Giannine seems to be finding them all. Which is a darn shame, because unless she can get the magic ring, locate the stolen treasure, answer the dwarf's dumb riddles, impress the head-chopping statue, charm the army of ghosts, fend off the barbarians, and defeat the man-eating dragon, she'll never win.
And she has to, because losing means she'll die--for real this time.
Wikipedia describes the beginning off the story which is also somewhat similar to what you remember:
Giannine receives a gift certificate for a Rasmussem Gaming Center as a birthday present from her father. When she arrives at the local center, a crowd from "CPOC," the "Citizens to Protect Our Children," has come for a demonstration against such games. She enters the arcade and gets hooked up to Heir Apparent, a single-player RPG. Giannine's character, Janine de St. Jehan, is the illegitimate child of the recently deceased King Cynric, who pronounced her heir to the throne, passing over three legitimate sons. Her task is to survive the three days (which will only last thirty minutes in the real world) before her coronation. Anytime her character dies, she will be sent back to the beginning of the game.
I can't find reference to her blood going bubbly and dissolving her but the first time she dies in game she describes it as feeling fizzy.
It didn't hurt. I felt fizzy, like an ice cube in a glass of ginger ale, all covered with carbonated bubbles. My knees gave out from under me, and my eyes grew heavy. When I opened them again, I was on the hill above the cluster of huts that was the village of St. Jehan, and my mother was calling, "Janine! Janine, come back to the house."
Heir Apparent, Chapter 5, "Simple Math"
Again it is mentioned the third time she dies of the fizzy bubbles, but no reference to them being blood. All the other times she dies she also mentions the fizziness but not that it is blood as far as I can tell.
I didn't have a chance to turn around. Something struck me hard on the back, knocking me face first to the ground. I cried out at the pain in my palms and knees—and at the back of my neck. I felt fizzy bubbles all over my skin.
Heir Apparent, Chapter 7, "Shuffle and Deal Again"
I found this by searching the TVTropes page The Game Come to Life(Warning!) and looking through the relevant results, Heir Apparent was on that list.
