The Bloodmage's free glyph isn't as useful as the glyphs from the other classes. It works well with classes that have good magic aptitude but little need for health restoration, like the Sorcerer, but thanks to the Power-Hungry feature, bloodmages don't really need it as much. The way to go with the Bloodmage is to get as many mana potions as possible and leave the blood pools from killed monsters untouched as long as possible. The bosses can be taken on using fireballs, HALPMEH, CYDSTEPP and/or poison (whatever works best) and with the help of bloodpool regeneration. You'll be able to cast a lot due to the mana potions' 100% regeneration, but the health loss from using a potion makes it more difficult to use several in a row, as you'll need to save up blood pools and/or health potions. Note that you won't be allowed to drink a mana potion if you do not have sufficient health.
Race & Deity Choices
Gnome or Elf are your ways to go here. As a Gnome you'll have a lot of Mana Potions and therefore a lot of mana. As an Elf you'll have more Mana overall but less Potions for regeneration. The Elf, due to having more overall mana, definitely has the advantage when trying to take on monsters without using potions. On the other hand, the Gnome will miss individual potions less, and can take on monsters that are even higher level than the Elf can without setting himself back too far against the boss. Against the boss, a Gnome who has many potions saved up will have more mana overall (by 25, at 5 glyphs converted), however, the Elf will have to pay less health to use up all his mana, and will be able to more effectively melee the boss in conjunction with any magical assault. Note that if the dungeon spawns with shops or Deities that allow for expanding maximum mana (such Mystera Annur), it favors the Gnome, while spawns and midfight leveling strategies that allow for more mana refills benefit the Elf more.
Mystera Annur should be your preferred Deity, and makes BLUDTUPOWA look significantly more useful, as you don't need to regenerate health as much if you aren't attacking enemies directly. If that one's not available you can still go with The Pactmaker. BLUDTUPOWA, if you can also pick up BURNDAYRAZ and APHEELSIK, also makes Tikki Tooki slightly more feasible since you can have an assurance of risk-free damage.
Level up by killing Gorgons and go for Serpents and Nagas only if you can kill them without getting weakened or poisoned (except you'll get a level up or use HALPMEH). Try to not use any Mana Potions until you're able to take on the bosses.
If you're around level 7 start attacking Medusa. Immunity to Death Gaze is helpful but not necessary. Just make sure to keep your Health up with bloodpools, potions and level up. Make sure to keep enough potions for the Jormungandr, who can be outlasted afterwards.
Crypt is tricky, as usual. Level up on Vampires and Zombies, if you can buy Soul Orb. Best combination is HALPMEH, BURNDAYRAZ and your bonus glyph, since you can quickly regain mana and heal yourself, instead of spending tiles for natural healing. In this dungeon mana-rewarding deity is crucial, since Frank has a lot of hit points. The Pactmaker is better, because he will let you attack with your weapon, while Mystera will make you rely on fireball solely. Sometimes it is better to heal and attack again, than to burn enemy. Begin with Tormented One, when you are about to hit level 7, burn him, level up, burn again and spend one potion to finish him. This will kick you almost to level 8. Explore to gather all resources. Kick Frank, burn him and level up. Begin to spend potions, but do not forget, that if your health is too low, you will be unable to drink mana potions. Blood pools and HALPMEH can solve this. If you have around 6-7 potions you will outlast Frank.