Saving text files to USB drive

As I understand, you mounted the USB device (the sdb1 partition) in the Peropesis filesystem, where the Peropesis-*-live.iso image was written. What you mounted should be an ISO file system. This system is a read-only file system. This means that it is not possible to write data to it.

As far as I understand, the files you create can only be saved to another/new built-in USB device, that has been previously formatted to the FAT32 file system.

But if you just want your newly created '.bashrc' file could work in the Peropesis filesystem, without reloading it first, this can be done by executing the bash program with --rcfile option. Example:
# bash --rcfile .bashrc

As you know, everything you created in the Peropesis file system disappears when you restart your computer. The only way to save is to copy these files to other media or send them somewhere using the internet.

If you still want to save your created files to Peropesis, which is on a USB drive, you should do it like this:

1. Mount the Peropesis-*-.iso to the file system (as I understood you did it in the /mnt directory). Example:
# mount /dev/sdb1 /mnt

2. Copy the contents of the /mnt directory to the newly created directory, eg /root/iso. Example:
# mkdir /root/iso
# cp -dpR /mnt/* /root/iso

3. Move the archived root file system from the directory /root/iso/images to the new directory fs. Example:
# mkdir /root/fs
# mv /root/iso/images/rootfs.xz /root/fs

4. Extract the rootfs.xz filesystem. Example:
# cd /root/fs
# xz -dc < rootfs.xz | cpio -idmv | rm rootfs.xz

Note. Since Peropesis is a super small system, there is no cpio archiver program in it. Cpio can be downloaded and installed. Example:
# wget https://ftp.gnu.org/gnu/cpio/cpio-2.14.tar.bz2 #(or by using browser links)
# tar -xvf cpio*
# cd cpio-2.14
# ./configure --prefix=/usr
# make
# make install

Something like that... Check is 'cpio' exist:
$ cpio --version

5. After unzipping roofs.xz, you should see the file system "/bin /boot /dev etc..." in the "fs" directory. Example:
# ls /root/fs

6. It is now possible to upload newly created files such as .bashrc to the file system. Example:
# cp -dpR .bashrc /root/fs/root

7. The newly prepared file system needs to be archived again. Example:
# cd /root/fs
# find . | cpio -R root:root -H newc -o | xz -9 --check=none > ../rootfs.xz

8. The archived file system needs to be moved to the /root/iso/images directory. Example:
# mv /root/rootfs.xz /root/iso/images

9. Next you need to create a new ISO image. Example:
# cd /root/iso
# export ISO=/root/iso
# mkisofs -z -R -l --allow-leading-dots -D -o \
../Peropesis2.iso -b isolinux/isolinux.bin \
-c boot.cat -no-emul-boot -boot-load-size 4 -boot-info-table \
-V "Peropesis-2.2-live" $ISO

Note. Since Peropesis is a small system, "mkisofs" program is still not included in it. "mkisofs" is part of the "cdrtools" software package. This sowtware has open source, so like cpio it can be downloaded and installed. Example:
# wget https://downloads.sourceforge.net/cdrtools/cdrtools-3.02a09.tar.bz2
# tar -xvf cdrtools-3.02a09.tar.bz2
# cd cdrtools-3.02
# make
# make INS_BASE=/usr install

Check is 'mkisofs' exist:
# mkisofs --version

10. If everything is fine, then you need to burn your newly created personal ISO to a new USB device and use it. Example:
# dd if=Peropesis2.iso of=/dev/sdx

If you haven't used it yet, I recommend using screen multiplier for making new filesystem and ISO. In this way, the screen can be divided into several windows, so it is much more convenient to work, especially when copying commands, for example from this post. Manual about it: https://peropesis.org/user-manual/#screen-manager-screen

For simplicity, all commands were executed with root privileges. I hope your question was about that.