Bloodlines are class levels and count towards your ECL. That means if you have 3 levels’ worth of bloodline, to reach your 18th level in wizard, you would need ECL 21st—which per Dungeon Master’s Guide page 206, you can get by reaching 210,000 XP. However, if your game is described by your DM as “non-epic,” this most likely means that no amount of XP is sufficient to reach ECL 21st—in which case you would never be able to reach wizard 18th while simultaneously having three levels’ of bloodline.
For what it’s worth, in my experience, precisely this rule, eliminating ECL 21st altogether, is extremely common, and also, for me, highly recommended. Actually, I strongly recommend not getting anywhere near 21st—the game breaks down long before then. Can happen as early as 7th level, in fact.