This tune is played on the fiddle but it sounds okay on guitar.
The melody is sung an octave lower than the guitar plays it.
h: These should be quickly hammered on from 2 frets below to add ornamentation to the melody.

E|------------------------------------------------------------------------|
B|-----------------------9-----------------------h14--14--12-------12-h14-|
G|-------------9---9-11-------h11--9------------------------13------------|
D|9-----9---11-------------------------11--9------------------------------|
A|------------------------------------------------------------------------|
E|------------------------------------------------------------------------|
  There was an old woman lived by  the sea shore, bow and balancce to  me 

|-------------12--12---------------------------------------------------|
|12----12--14-------14--12---h14-12--12--------------------------------|
|---------------------------------------h13-11------11-11--11-11-------|
|-----------------------------------------------14-----------------14--|
|----------------------------------------------------------------------|
|----------------------------------------------------------------------|
 There was an old woman lived by the sea shore, the number of daughters

|--------------------------------------------12------------|
|-----------------------------------s-----12---h14---12----|
|11-h13-11---------p-------9----11--/13-----------------13-|
|----------14----11\9--9------9----9-----------------------|
|----------------------------------------------------------|
|----------------------------------------------------------|
 One two   three four, and I'll be   true to my love if my

|--h-----7--7----7-----|
|7-/-9-----h9---h9p7---|
|--------------------9-|
|----------------------|
|----------------------|
|----------------------|
 Love'll be true to  me