How old is the 9-speed bike? If it’s 105 or better, than the bike is likely to be a 2004 or older, which means that if you want to upgrade from 9sp to 11sp, you’ll end up needing:
- new crank
- new cassette
- new chain
- new rear derailleur (and likely new front derailleur)
- new shifters
- new rear hub (or wheel, which will likely be cheaper if you’re not doing the labor yourself)
- new handlebar tape
Additionally, new shifters are designed for 31.8mm diameter bars, and if the bike is 20yrs old, it’ll still have much skinnier handlebars. I don’t know if new shifters can be cranked down enough to fit on the older diameter, so you might need to budget new bars and stem in, as well.
all that without labor is likely to be upwards of $750, or nearly $1k with a decent bar/stem combo…