Remove the BB first.
Drill a 7mm hole in the middle of the bottom, deburr both sides and refit BB. Being Ti it will eat your HSS drill-bits, so use a 3mm starter before the 7mm and expect to discard or sharpen them afterwards. Do not use a masonry drill-bit.
Go ride.
Check it is clear every now and again as it can block with mud.
Alternatively block off the top, down and chainstay tubes where they join the BB with builders expanding foam.
With Ti you do not have a potential rusting/corrosion problem.
I have a 22 year-old steel frame that I sprayed internally with a thin oil, then sealed all the external holes in the seat and chainstays.
Greased the seatpost and the BB threads heavily and no water in the BB shell, ever. Worn 3 XT square tapers out in 100,000 miles.
PaulD