Hello!
Just expanding on yohy?!'s points above, a few suggestions and points about upgrading and flying business class relatively cheaply:
1. Buying Miles from an airline program
As mentioned above, certain programs offer the ability to purchase miles (occasionally with a bonus miles or at a discount). American Airlines AAdvantage is good for travel on oneworld airlines (and a few non-oneworld partners like Etihad Airways) and Avianca Lifemiles is good for Star Alliance airlines.
These tickets are generally only available if there are award seats available on the flight, so you may need to be flexible with the dates and routes you want to fly. For example, I was looking at a PER-LHR journey a couple of years ago and the only available option in business was Perth-Sydney-Tokyo-London.
Before using this option, it's important to check how many miles you will need (most of the 'award charts' quote based on one-way tickets so you'll often need to double it for a return journey), how much it will cost and how that compares to the cost of a cash ticket.
Pros:
Confirmed business class seat upon booking
Significantly cheaper than buying the ticket outright
Cons:
Availability is subject to award seats being available, so will probably not work during peak travel times or routes (school holidays or in-demand routes) and flexibility with travel dates and routes is required
Miles required are subject to change with short notice
Purchase subject to currency fluctuations and foreign transaction fees
2. Earning miles from credit card offers / everyday spending then using them for award tickets and upgrades
You can earn a lot of miles very quickly through credit card bonus offers and daily spending on a credit card that is linked (or allows transfers to) a frequent flyer account.
These miles are then redeemed for either 1) An award seat outright if available, 2) Upgrade requests (fixed number of miles required) or 3) Upgrade bids (flexible number of miles required but subject to competing bids).
With upgrade requests, many airlines (including Qantas) will process them based on your status with the airline so if you do not hold status you will be very low on the pecking order. Qantas also process upgrade requests before considering point bids.
Pros:
Earn hundreds of thousands of miles in a short space of time
Frequent flyer redemptions can be good value because business award tickets and upgrades are usually only 2x the cost of economy award tickets
Cons:
Applying for multiple cards in a short space of time will hurt your credit rating significantly
Outright award seats subject to availability (as per above)
Upgrade award seats may be processed based availablilty and then status with the airline so not guaranteed (and very low chances unless you are a top-tier member)
Some benefits may not be provided (e.g. extra baggage allowance) if processed at airport
3. Cash upgrade bids
As you have mentioned most airlines now offer the ability to offer cash upgrade bids online, or occasionally, buy up at the airport (I think British Airways offers this).
Pros:
Cheaper to purchase as airlines are trying to upsell otherwise empty seats
Cons:
Airline retains discretion to reject bid so not guaranteed
Often processed last as airlines want to sell seats to last minute business flyers
Some benefits may not be provided if processed at airport (as above)
4. Fly to/from cities outside Australia
Unfortunately in Australia we are hit with high business class airfares compared to other parts of the world. Flying out of particular places in South East Asia or flying the trip in reverse (e.g. Europe-Australia-Europe) is often significantly cheaper than an Australian-based departure. Good places for these journeys are Bangkok, coughet, Manila and Colombo (in Asia) and Oslo, Stockholm and Copenhagen (in Europe).
You can then book a separate cheap ticket to position to these locations.
Pros:
Much cheaper than paying for business class out of Australia
Confirmed business class seat for the long-haul portion of your journey
Cons:
Need to buy two separate tickets, which means you may not be protected in the case of a delay
May need to collect your bag at the intermediate stop - so will need to set time aside to do so (and visa costs to enter the country, if applicable). I tend to spend the night in the intermediate stop just to provide buffer for delays.
5. Mileage brokers
Generally, the terms and conditions of a frequent flyer program prevent you from transferring miles (except, in some cases, between family members). Buying and selling miles comes at a huge risk as accounts can be suspended or closed and miles forfeited (and in such cases, you have no recourse against the seller or the airline). I'm not aware of any airline that permits the transfer of miles from a third party.
I hope this helps!