I'd probably start with just asking the GM to assign a BAB progression and saving throw progression to the Blood Hunter class to replace its proficiency bonus for attack rolls and saving throws. Also need to convert the skill list.
Any abilities that key off of proficiency bonus can probably just use the 5E proficiency bonus.
For spells, if there's a Pathfinder version, use it. If not, check with your GM first.
For the +2 ability score boosts that the 5E classes get at various levels, we allow the character to choose 2 Pathfinder feats (but we give all characters a feat every level as a houserule). This could be scaled back to just a bonus feat.
Our group does this with most 5E classes in our Pathfinder game and it works well. Originally, we were going to convert to 5E, but in the end we decided that we wanted the AD&D 1&2E classes, D&D 3X, and Pathfinder versions of the classes all available for play and since I owned mostly 3X and PF books and the adventures I plan to run were written in 3X/PF, I decided we'd stay there. The 5E classes work fine in our game (YMMV). Even 5E spells seem to work OK (though some 5E cantrips are higher powered and should probably be 1st level spells in PF.
I like the Blood Hunter, but have never played it or seen it played, other than online.