I agree with Hyomin. Check out Chae's and Cetonis' Bard guide. It is quite wordy, however, but it does go in depth on how to play in many situations. Also, Miyuri's opener is a good alternative opener that works just as well.
One thing I noticed in your opener is that you used Barrage with Empyreal Arrow very early. You should try to hold onto Barrage and fish for Reflugent Arrow procs to use with Barrage. You can get in about 4 to 5 Heavy Shots to fish for Reflugent Arrow before Raging Strikes runs out. You want to delay your strongest attacks a little bit to take advantage of raid buffs like Trick Attack.
Generally speaking, it is important that you snapshot buffs just before they run out. I noticed you did not use Iron Jaws a 2nd time in the opener. I believe you should try to Iron Jaws near the beginning of Raging Strikes and once again near the end of Raging Strikes. In raids, party buffs like Chain Strategem, Trick Attack, Battle Litany, etc. will be running out at about the same time as Raging Strikes. You want to snapshot these buffed dots. 45-50 seconds of buffed dots is quite important in the opener since that potentially gives you more Pitch Perfect and Bloodletter Procs.
There were some minor GCD clipping parts like triple oGCD at the end (Barrage -> Empyreal -> Pitch Perfect). Try to double-weave two oGCDs at the most. Also there were some parts where you let Bloodletter stay unused for about 3 seconds, which is a potential DPS loss. Try to always keep Bloodletter on cooldown (spam that button during Mage's Ballad). There were also some downtime with the 3 songs. Try to get about 30s Wanderer, 30s Mage's, 20's Army's.
There can be some variance with Bard since you can get low proc rates vs high proc rates. Just keep practicing and try to find possible GCD downtime or missed buffs you did not realize occurred.