I've tried to estimate I-band magnitudes for Tycho and Hipparchos
stars in the past. Here's one set of notes I made, for the Tycho-2
catalog.

# This file contains information on a subset of stars from the Tycho-2
# catalog. The stars were selected to be good photometric references,
# by satisfying all of these conditions:
#
# magnitude Bt 1.0 (discards incorrect "zero"
magnitudes)
# magnitude Vt 1.0 (discards incorrect "zero"
magnitudes)
# uncertainty in Bt 0.20
# uncertainty in Vt 0.20
# color -0.2 (Bt - Vt) 1.8
# no other Tycho-2 star within 20 arcsec
# "solution" flag does not indicate double-star astrometric
solution
#
# (This differs from an earlier subset in the uncertainty in magnitude:
# 0.20 versus 0.05 mag. Almost all stars have larger uncertainty in
Bt)
#
# For each such star, I estimated Johnson-Cousins magnitudes based on
# on message from Arne Henden:
#
# B = Bt + 0.018 - 0.2580*(Bt - Vt)
# V = Vt + 0.008 - 0.0988*(Bt - Vt)
# I = Vt - 0.039 - 0.9376*(Bt - Vt)

You may also find it worth while to look at

http://stupendous.rit.edu/tass/catal...s.html#vi_type