How to match a string on a file using pure bash?

You can do it. But it is a really, really bad idea. It will be far slower (as in orders of magnitude slower) than grep and less portable since it depends on features of a specific shell (Bash).

This would print out lines matching a regex pattern given as the first argument, similarly to grep pattern:

#!/bin/bash -

regexp="$1"
ret=1
while IFS= read -r line || [ -n "$line" ]; do
  if [[ $line =~ $regexp ]]; then
    printf '%s\n' "$line"
    ret=0
  fi
done
exit "$ret"

Save that as foo.bash and run like this:

foo.bash pattern < inputFile

Or using standard sh syntax, looking for a fixed string and not a regex:

#!/bin/sh -

string="$1"
ret=1
while IFS= read -r line || [ -n "$line" ]; do
  case $line in
    (*"$string"*)
      printf '%s\n' "$string"
      ret=0
  esac
done
exit "$ret"

(Replace the printf with exit 0 to get behaviour similar to grep -q.)

Just to give you an idea of how slow it is, I created a file with just 10001 lines, the first 5000 being foo, then a single bar and then another 5000 foo :

perl -e 'print "foo\n" x 5000; print "bar\n"; print "foo\n" x 5000;' > file

Now, compare the times for grep and the script above:

$ time grep bar < file
bar

real    0m0.002s
user    0m0.002s
sys     0m0.000s

$ time ./foo.bash bar < file
bar

real    0m0.116s
user    0m0.101s
sys     0m0.016s

As you can see, even with this tiny file, the difference is noticeable. If we try with a more substantial one, the time the script takes turns almost unbearable:

$ perl -e 'print "foo\n" x 500000; print "bar\n"; print "foo\n" x 500000;' > file


$ time grep bar < file
bar

real    0m0.004s
user    0m0.000s
sys     0m0.004s


$ time ./foo.bash bar < file
bar

real    0m11.306s
user    0m10.117s
sys     0m1.188s

However, this is partly because Bash is slow. The standard sh version runs a bit faster with Dash:

$ time dash foo2.sh bar < file
bar

real    0m3.467s
user    0m2.113s
sys     0m1.353s

However, it's still a difference of three orders of magnitude. Multiple seconds for the scripts, against the near-instant grep. And this is still a file with only a million lines and ~4MB in size. I hope you see the problem...