It has two possible meanings (at least according to Google):
a person's inherent qualities of mind and character.
"a sweet-natured girl of a placid disposition"
"the book is not recommended to readers of a nervous disposition"
synonyms: temperament, nature, character,
constitution, make-up, grain, humour, temper, mentality, turn of
the way in which something is placed or arranged, especially in relation to other things.
"the plan shows the disposition of the rooms"
The latter could work as a metaphor: the orientation of his rooting in the field. It would be a bit of a pun too - alluding to 'field' in the more common sense of the word. (Root is a bit of a pun there after all.)
However, I think it is mostly if not completely using the first definition because it seems to go better with dedication. It doesn't quite work as that in my opinion (so I can understand your confusion):
"My inherent qualities of mind and character have become more rooted in this field" doesn't really make sense but certain synonyms are clearer: "My nature|mentality has become more rooted in this field"
I think it really just means "My thoughts and feelings" (or indeed interests, passions as you suggest) and is a slightly fancy and incorrect way of saying it. That there is the metaphor/pun however might have been the motivation behind using it and it makes it good in my opinion: I'd generally prefer a slightly amusing/confusing sentence to a boring/perfectly clear one (except when I'm in a hurry).