I'm an aviation enthusiast with a base in Vietnam, so I'm familiar with the airline business from a frequent flyer perspective.
Reason 1: No Clear Niche
Bamboo Airlines struggled to define its place in the market. It wasn't the flag carrier like Vietnam Airlines, nor was it a full-service airline. Instead, it occupied an awkward middle ground between budget and premium services.
Reason 2: No Room for a Budget Airline
Budget airlines, henceforth called Low Cost Carriers (LCCs) or Ultra Low Cost Carriers (ULCCs), avoid competition and expensive airport fees by flying to secondary airports. You can read this article called Ryan Air will never fly to Heathrow.
However, this is not possible in Vietnam, which only has 20 airports, most of which either have 1-3 daily flights or 3-4 flights per week. There's only 3 major cities in Vietnam, Hanoi, Ho Chi Minh City (HCMC), and Da Nang. People going to destinations nearby Hanoi or HCMC will just fly to the major city and take a cheap "limo" (e.g. passenger bus/van) to their final destinations. As such, regional airports see very little traffic. It's all consolidated into the big airports. Now, it's still possible to have budget airlines in Vietnam. There's VietJet and Pacific Airlines (the latter of which is 98% owned by Vietnam Airlines, previously named Jetstar Pacific), but that's already so much competition. So much competition that Pacific Airlines recently returned all their leased aircraft and are now going to be leasing aircraft from their parent company.
VietJet and Pacific are terrible to fly on, hard seats and tiny legroom, but they tend to be around 1-1.3 million VND in total air fare each way, while Vietnam Airlines is often 1.7-2.5 million VND (both including taxes, actually, the base fares tend to be below 100 thousand VND, taxes & fees are the majority of the ticket cost).
So if Bamboo Airways wanted to be a budget airline, they'd have to compete with VietJet and Pacific Airlines on very high volume and high supply routes (Hanoi to HCMC has around 37 daily flights from Vietnam Airlines and around another 25 from Vietjet). These budget airlines need the demand from the popular routes but there's only so much to go around.
Reason 3: Unable to Compete as a Full-Service Airline
I'm not pretending that Vietnam Airlines (VN or VNA) is so great. The IT system is bad (if you thought delta was bad, trust me VN is in the stone age), and the one time Non Stop Dan tried reviewing them from Incheon, their plane got swapped from a widebody to an A320 narrowbody, meaning their business class lie flat seat got replaced with a chair that looks like your mother in law's recliner.
Reason 4: Lack of Alliance Membership
The real reason it can't be a full service airline is that it doesn't have the perks of a full service airline. Vietnam Airlines is the only Vietnamese airline in an alliance (SkyTeam). Other airlines have some codesharing agreements, but if people are looking to fly to Vietnam, they're going to fly with their OneWorld, Star Alliance, or SkyTeam airlines. OneWorld has Cathay Pacific just 1 hour away from Hanoi with a wonderful airport, and they have Japan Airlines which operates many North America to Asia trips. OneWorld also has Qatar Airlines, which brings many people from the Americas and Europe into Asia.
Then we have Star Alliance. World class Singapore Airlines (SQ) is just 2 hours away from HCMC (SGN). SQ is beloved by many and they even fly to both JFK and Newark! They have amazing premium hard products. Then there is Asiana Airlines (in Korea) and ANA in Japan, both also in Star Alliance and both feed traffic from North America into Asia (Korea and Japan are the Asian countries closest to North America, other than Russia of course). Then there is Thai Airways, which operates nice flights from Europe into the South East Asia region (SEA).
As you can see, there are many options for travelers, but we're not done yet. Like I mentioned earlier, SkyTeam has Vietnam Airlines as a member, but also Korean Air. Korean Air serves as a vital hub to feed traffic from NA into Asia. While Delta doesn't fly to Vietnam, they do fly into HND (Japan) and ICN (Korea), which Vietnam Airlines flies to. Korean Air also has direct flighs from Korea to Boston and many US cities. SkyTeam doesn't have many partners in Asia asides from Garuda Indonesia and two Chinese airlines, but they do have many partners in Europe. So NA traffic goes through Korea or Japan first via Delta or Korean Air, then by Korean Air or Vietnam Airlines, and Europe goes from Air France direct to Vietnam, or other European Locations operated directly by Vietnam Airlines.
Basically, if you're travelling to Vietnam, you're going to stick with your current airline alliance. There is plenty of connectivity to Vietnam, so if you're not going to be a full service airline, then you shouldn't try, because Long Haul Low Cost Carriers don't work.
Also, don't forget that intra-Asia traffic has many budget airlines already. AirAsia, Jetstar, and many others fly to Vietnam.
The Awkward Middle Ground
So they're not a budget airline, but they have the ticket prices closer to a full service airline without many of the amenities (although they are generous with status matching people).
What weird middlepoint are they going for? We already know "premium" in a LCC doesn't work (just look at how empty SkyBoss is in VietJet), they can't be a Long Haul (LH) LCC, they can't be a budget airline, and they don't have what it takes to compete with full service airlines. They can't have a niche by only operating to unpopular locations. So why bother? I wish I had the connections of whoever drafted their business plan, because I have many crappy business ideas better than this.