How can I remove all text after a character in bash?

An example might have been useful, but if I understood you correctly, this would work:

echo "Hello: world" | cut -f1 -d":"

This will convert Hello: world into Hello.

In Bash (and ksh, zsh, dash, etc.), you can use parameter expansion with % which will remove characters from the end of the string or # which will remove characters from the beginning of the string. If you use a single one of those characters, the smallest matching string will be removed. If you double the character, the longest will be removed.

$ a='hello:world'

$ b=${a%:*}
$ echo "$b"
hello

$ a='hello:world:of:tomorrow'

$ echo "${a%:*}"
hello:world:of

$ echo "${a%%:*}"
hello

$ echo "${a#*:}"
world:of:tomorrow

$ echo "${a##*:}"
tomorrow

egrep -o '^[^:]*:'

$ echo 'hello:world:again' |sed 's/:.*//'
hello