Bangladesh Air Force would be hopelessly outmatched by Myanmar and its Mig 29 fleet.
The SAM capability of Myanmar is infinity times better than Bangladesh which relies totally on AAA.
Navy the less said the better.
On the ground however it could go either way. There have been past reports of Bangladesh winning border skirmishes hands down.
You are right on airforce but not on either Navy or Army.
BD Navy is the only one with subs and it is also the only one that has proper SAMs on it's ships. Myanmar has man-portable SAMs on their ships lol.
BD Airforce and Army is equipped with the FM-90 which has multi-target capability and range of 15km. While this cannot provide area defence, it is enough to defend targets such as airbases and army barracks from MAF attacks.
Medium range SAM such as LY-60 will be coming soon as a tender was put out for that earlier this year
BD army is far more professional than Myanmar and as you have noted it has won border clashes hands down. It is safe to safe that if you take out the MAF, BD Army will roll into Arakhan with ease.
Onto the air-force lastly. This is where it gets interesting. For some bizarre reason, Myanmar has decided to purchase 16 JF-17s which will become prey to the 12 SU-30SMEs that should arrive in BD by 2019. The 31 Mig-29s that are not even that modern will not fare much better.
So on current trends BD military will totally dominate Myanmar one by 2019.
Myanmar just seems to buy anything without any long-term plan, whereas BD maybe spends too much time but in the end gets way better equipment for the same money.