Since you requested bash only:

#!/bin/bash

string="$2"

while read line ; do
    if [[ ${line:0:1} == ">" ]] ; then
        header="$line"
    else
        seq="$line"
        if [[ "$header" == *"$string" ]]; then
            echo -e "$header""\n""$seq"
        fi
    fi
done < $1

Put it in a script file and run it like:

$ bash parseheaders.sh seqs.fasta .4

Some of my own test data:

$ cat seqs.fasta
>tpg|Magnaporthiopsis_incrustans|JF414846
ACTGTAGTAGCTACGATCGATCAGATGATCACGTAGCATCGATCGATCATCGACTAGTAGATCACTCGACATAGATCCACATCAATAGATCATCATCATCATAATCGATCACTAGCAGC
>tpg|Pyricularia_pennisetigena|AB818016
GCAAGNTTCATGACGATGTAGAATGGCTTATCGAAGGGAGCAGGCCAGGGATTGAGGTCCGTCTCACGGGTTGGCTTCACTCCCCCACTGCCAGCCCTCTTGCTGCAACTCCACCAGAA
>tpg|Inocybe_sororia|EU525947
AACCANGCCGCGACGGCGGTGCGATCGGGAAACGCGGCGGTGGCGGAGGAATCGGCCATCCTTCACCATATCGGCCAAGGATTGTGGTTCCTGTAGGGCTCGCGCAGCCCAGGACGCGC

$ bash parseheaders.sh seqs.fasta 947
>tpg|Inocybe_sororia|EU525947
AACCANGCCGCGACGGCGGTGCGATCGGGAAACGCGGCGGTGGCGGAGGAATCGGCCATCCTTCACCATATCGGCCAAGGATTGTGGTTCCTGTAGGGCTCGCGCAGCCCAGGACGCGC

grep '^>.*4$' -A 1 --no-group-separator in.fa