The readline commands that you are looking for are the
Search forward through the history for the string of characters between the start of the current line and the current cursor position (the point). This is a non-incremental search.
Search backward through the history for the string of characters between the start of the current line and the point. This is a non-incremental search.
Binding these in your
.inputrc, like so:
"\e[A": history-search-backward # arrow up
"\e[B": history-search-forward # arrow down
will allow you to enter the first characters of a command, and then use the Up and Down keys to move through only those commands in your
.bash_history that begin with that string.
For example, entering
vi and the Up would take you to the first previous command beginning with
vim somefile. Entering Up would take you to the next previous instance, and so on.
You can read more about all of the readline bindings here: