Here's an exercise that will help dexterity.
Note that the fingering, descending, is played in the same sequence as ascending (up - 1-2, down 1-2 NOT 2-1). Start at the higher frets (say 10, 11, 12 and 13) and use the fingers shown in the diagram (1 finger per fret, so 1 - i.e. index finger - on fret 10, 2 on fret 11, 3 on fret 12 and 4 on fret 13):

|----------------------1-2----------------------|
|------------------1-2----1-2-------------------|
|--------------1-2------------1-2---------------|
|----------1-2--------------------1-2-----------|
|------1-2----------------------------1-2-------|
|--1-2------------------------------------1-2---|

|----------------------3-4----------------------|
|------------------3-4----3-4-------------------|
|--------------3-4------------3-4---------------|
|----------3-4--------------------3-4-----------|
|------3-4----------------------------3-4-------|
|--3-4------------------------------------3-4---|

|----------------------2-3----------------------|
|------------------2-3----2-3-------------------|
|--------------2-3------------2-3---------------|
|----------2-3--------------------2-3-----------|
|------2-3----------------------------2-3-------|
|--2-3------------------------------------2-3---|

|----------------------1-3----------------------|
|------------------1-3----1-3-------------------|
|--------------1-3------------1-3---------------|
|----------1-3--------------------1-3-----------|
|------1-3----------------------------1-3-------|
|--1-3------------------------------------1-3---|

|----------------------2-4----------------------|
|------------------2-4----2-4-------------------|
|--------------2-4------------2-4---------------|
|----------2-4--------------------2-4-----------|
|------2-4----------------------------2-4-------|
|--2-4------------------------------------2-4---|

|----------------------1-4----------------------|
|------------------1-4----1-4-------------------|
|--------------1-4------------1-4---------------|
|----------1-4--------------------1-4-----------|
|------1-4----------------------------1-4-------|
|--1-4------------------------------------1-4---|

|----------------------2-1----------------------|
|------------------2-1----2-1-------------------|
|--------------2-1------------2-1---------------|
|----------2-1--------------------2-1-----------|
|------2-1----------------------------2-1-------|
|--2-1------------------------------------2-1---|

|----------------------4-3----------------------|
|------------------4-3----4-3-------------------|
|--------------4-3------------4-3---------------|
|----------4-3--------------------4-3-----------|
|------4-3----------------------------4-3-------|
|--4-3------------------------------------4-3---|

|----------------------3-2----------------------|
|------------------3-2----3-2-------------------|
|--------------3-2------------3-2---------------|
|----------3-2--------------------3-2-----------|
|------3-2----------------------------3-2-------|
|--3-2------------------------------------3-2---|

|----------------------3-1----------------------|
|------------------3-1----3-1-------------------|
|--------------3-1------------3-1---------------|
|----------3-1--------------------3-1-----------|
|------3-1----------------------------3-1-------|
|--3-1------------------------------------3-1---|

|----------------------4-2----------------------|
|------------------4-2----4-2-------------------|
|--------------4-2------------4-2---------------|
|----------4-2--------------------4-2-----------|
|------4-2----------------------------4-2-------|
|--4-2------------------------------------4-2---|

|----------------------4-1----------------------|
|------------------4-1----4-1-------------------|
|--------------4-1------------4-1---------------|
|----------4-1--------------------4-1-----------|
|------4-1----------------------------4-1-------|
|--4-1------------------------------------4-1---|

As you get better, you can start to play on lower frets, which will help increase your hand span.