Eligibility can vary between health boards however if you have a history of aromatase inhibitor treatment or any other risk factors such as previous smoking, low weight, alcohol, steroid use, malabsorption, parental history of hip fracture etc it is certainly worth asking your GP for a referral.
This may also depend on what the previous one showed - if you had bone loss at that time it is more likely they will be willing to repeat this.
If the answer is no then you haven't lost anything. You may also need a GP referral to obtain one privately, I am not sure there are that many places you can self refer for a DEXA, so the same letter can be used for this.