IANAL, and it'll depend on the current legal structure of your start-up, and the jurisdiction you're in, and how formal you are with your co-founder about such things, and the funder's requirements and preferences, and etc. etc. etc... But you'll very likely have to spend a lot of time with lawyers (who ain't free) and your funder, and paperwork - discussing & planning & doing stuff which does nothing to actually bootstrap you faster or better. Plus figuring out what the heck is worth spending the $350k on. Plus ongoing regular formal reporting & interactions with your funder.

It's impossible for me to quantify how much $cost & time & emotional effort that'll be - but it's extremely likely to be substantial. And for what? You described what your start-up needed as "a lot more time & effort". Not "capital investment".