The direct losses you could experience in a bond-bubble burst (which is a real possibility but hardly a certainty) are of the following sorts:
- Default risk. The issuer of the bond could decide not to pay you back. This isn't usually a problem for government bonds, and even when it is a problem nations in trouble have preferred to pursue some sort of restructuring or "default lite" to outright default where you lose all your principal, but loss of principal is a risk and the reason for the existence of the credit-default-swap market you may have heard about. (Greece actually restructured its debt in 2012, adversely impacting its bond holders; bondholders have also suspected that Italy, Spain, and other troubled Euro-zone nations with debt problems may pursue similar courses).
- Interest rate risk. If you own a bond that has not yet matured (or a bond ladder or bond fund, which is continually rolling over and will always have components which have not yet matured) then when interest rates rise, you will not be able to sell the bond for as much money. This is not a problem if you hold all your bonds to maturity or hold all your bond funds indefinitely.
- Inflation risk. Sure, you receive your money when the bond matures, but the money isn't worth as much anymore. A rapid increase in inflation is one of the most probable potential reasons you could expect bond prices to fall and interest rates to rise to begin with.
You could also experience indirect losses, in the form of reduced values of other assets like stocks, real estate, commodities, or other investments, as the broader economy feels the effects of this bubble bursting and slows down. (This is possible collateral damage from any crisis, and not of bonds in particular.) In particular, businesses which rely on borrowing money at low interest rates will be at serious risk, because lower bond values and higher bond interest rates are essentially the same thing. Businesses which are closely related to borrowed money (e.g. companies that construct houses, or banks which lend money) will also be hit.
Hedges against this sort of a bubble-burst are tricky, and depend on your goals. If you were interested in bonds to begin with it's probably because of relatively stable values and low-but-positive returns. Certain commodities might perform well in this sort of turmoil, but industrial commodities (silver, platinum, palladium, copper, etc) may suffer if the economy suffers, gold is seeing its own possible-maybe-bubble-who-knows and will undoubtedly be subject to violent price swings in times of turmoil, and commodities generally have slightly negative rates of return in the meantime while you're holding them. Cash is safe from default risk and interest rate risk, but offers limited protection from inflation risk over the long term. (In the short term, it offers you a better chance to get a better interest rate if inflation hits and rates rise.) Short-term bonds are least subject to default and interest rate risk of bonds.
If you are a long-term investor, your best bet may be equities, especially equities of companies which can best weather an economic downturn, consumer-staples and the like, and which offer dividends that could be reinvested while the stock is depressed (for greater gains later). If you have real estate and rental income in a relatively stable housing market, or if you own your own home and treat the savings on rent as an investment (a valid approach, to some extent), then it might also keep its value in an inflationary environment, but only over the long term. Actually, a fixed-rate mortgage is an effective hedge against rising interest rates and rising prices, as the debt becomes cheaper to service in real terms; when savers lose, borrowers win. But short-term losses from housing-market issues remain a possibility.