As for Indonesia:
Travel in Indonesia isn't easy. But it is cheap.

As anywhere, the costs are relative to how close you live to the local customs. These break down into 5 areas:
1) Food
2) Lodging
3) Local transportation
4) International travel, across borders
5) Splurges -- sightseeing/resort stays

My wife and I crossed the Nusa Tenggara islands (Bali, Lombok, Sumbawa, Flores) ten years ago -- not on bicycles, however. I wouldn't expect much change in cost for food and lodging. Even for local transportation. Losmen (guesthouse) under $5 per night, meals $2-4. Two people easily survive on US$25 per day, and half of that is for transportation, which for you would be minimal with bicycles. The biggest expense would be inter-island ferries (can't remember, but probably on the order of $10 apiece, I'm sure they'd charge for bikes, too). But the ferry rides are worth it all by themselves, it's easily the best way to share a Indonesian day with locals.

(Bali is a special case. Anywhere near the resorts and beaches, travel can be prohibitively expensive -- and frustrating for travelers who are used to doing things on their own. This is the one island in Indonesia where my rip-off radar went red. Away from the resort beaches, it's paradise, but still expensive by Indonesian standards.)

Then there's air travel.... Flights are expensive, even inter-island flights which are with the minor Indonesian airlines; small planes, and I wouldn't expect bicycles to be accepted as luggage (of course, $$$$ could convince them...) However, distances aren't large, so you could fly two or three times for the same cost as one trip to Nepal, for instance.

Lots of travelers to Indonesia grab a ferry to Singapore or Malaysia for a cheap visa renewal. This, of course, is easiest from Sumatra or Bintan (the islands near S'pore and M'sia). You could do the same by flying -- to S'pore, M'sia, Phillipines, or Darwin -- and take a week "vacation" from the tour, but flying costs a lot more. With good planning, you could leave your bikes and gear in a trusted hotel, and return from the visa hop.

These are all just ideas... And would work no matter what region you travel to. Local flights -- domestic flights between cities in any given country -- are hard to book, expensive, possibly on small planes (limited baggage space), and depending on the local culture can be a nightmare to negotiate (Indonesia, for instance, still hasn't entered the information age, bookings and confirmation are best done face-to-face). That's all part of the charm. Travel in many parts of Asia is a lesson in patience. Trying to keep to a schedule can be very very expensive. Learning to adapt to this is one of the great rewards of travel.

International flights should be a lot easier to shop for, and a lot easier to book. Every Asian country seems to have a city or district with cheap travel agents -- usually where the embassies and consuls are. Getting visas and air tickets is usually pretty quick and cheap, as long as you're flexible -- a week, maybe, instead of a day. Just remember that bikes and baggage might limit your choices, and depending on the airline might add a lot to the cost.

I think I can understand your gf's aversion to Indonesia. Most people identify with Java and Bali, but those are extremes. But still should be experienced. Lombok and Flores are both corners of paradise. You can lose yourself on each one for months. The chain of ferries to cross these islands makes it a unique trip. Lombok is half Hindu-mystic and half laid-back-secular-Muslim. Flores, Christian and a former Portugese colony, feels like a transplanted Mexico. Sumbawa is a stark interlude: a desert scrub island and very staunch Muslim. Where else can you find all this, just by stepping off another ferry?

But I'm not trying to convince you... I just don't know enough about India, Nepal, and Tibet. Other posters can help you there. As far as cost, I'd guess that Laos and Cambodia are on the same order as Indonesia (Cambodia can be very expensive if you don't stick to local customs); Thailand 50% higher; Malaysia another 2x higher, and Singapore pretty close to Australia. Not surprisingly, the ease of travel in each country follows the same scale. This includes "confronting the crazy sections" of road -- the poorer the country, the poorer the infrastructure, the more concentrated the chaos on the roads...

-- Mark