What option are you willing to take?
If you just want to buy, there are two different type of bow for lvl 50. The Alesone Songbow (the one you mentioned) is pretty inexpensive and has very good damage/ATK base but seriously lack in Acc and Crab Bow which is weaker but has shorter delay and meldable (add Materia). In 1.22a or maybe later, you can also buy a very expensive Class Only (can't use as BRD) bow that is both stronger and meldable. Additionally they also said that sometimes after 1.22a there will be craftable (hence buyable) Job AF Bow (like the BRD NPC has most likely).
If you are willing to run instances, you can get a somewhat better than Normal Quality clean Crab Bow in Dzemael Darkhold, but it is not Meldable. You can however trade it for 1,000 Grand Company Seals.
If you are willing to grind Company Seals, there is a lvl 50 Ul'dahn Longbow purchase for 4,500 Flame Seals as a Recruit (not officially joining any). Once you are Inducted/Officially joining any of the Company and work your way up to Sergeant Third Class, you can buy a better lvl 50 Bow for 4,500 Seals. If you are more willing, you can work your way up to Chief Sergeant and buy an even better lvl 50 bow that get a big Sanction bonus for 6,000 Seals. There is an NPC in the GC Hall that give Sanction bonus, it last 3 hours and you can retake Sanction by returning and talking to that NPC again, however it instantly wears off the moment you die.