How to list the open file descriptors (and the files they refer to) in my current bash session

Yes, this will list all open file descriptors:

$ ls -la /proc/$$/fd
total 0
dr-x------ 2 isaac isaac  0 Dec 28 00:56 .
dr-xr-xr-x 9 isaac isaac  0 Dec 28 00:56 ..
lrwx------ 1 isaac isaac 64 Dec 28 00:56 0 -> /dev/pts/6
lrwx------ 1 isaac isaac 64 Dec 28 00:56 1 -> /dev/pts/6
lrwx------ 1 isaac isaac 64 Dec 28 00:56 2 -> /dev/pts/6
lrwx------ 1 isaac isaac 64 Dec 28 00:56 255 -> /dev/pts/6
l-wx------ 1 isaac isaac 64 Dec 28 00:56 4 -> /home/isaac/testfile.txt

Of course, as usual: 0 is stdin, 1 is stdout and 2 is stderr.
The 4th is an open file (to write) in this case.

Assuming you want to list the file descriptors that are attached to any terminal, you can use lsof/fuser or similar like:

$ lsof -p $$ 2>/dev/null | awk '$NF ~ /\/pts\//'
bash    32406 foobar    0u   CHR 136,31      0t0      34 /dev/pts/31
bash    32406 foobar    1u   CHR 136,31      0t0      34 /dev/pts/31
bash    32406 foobar    2u   CHR 136,31      0t0      34 /dev/pts/31
bash    32406 foobar    3u   CHR 136,31      0t0      34 /dev/pts/31
bash    32406 foobar  255u   CHR 136,31      0t0      34 /dev/pts/31

These tools basically parse /proc, so you can just access /proc/$$/fd/ too e.g.:

ls /proc/$$/fd/*

lsof -a -p $$

Network fd only:

lsof -i -a -p $$