There's nothing legally stopping the bond market from increasing indefinitely, but before investors will be willing to buy a company's bonds, they must be confident that the company can pay back the money with the interest promised. Even with 0% interest, if a company borrows too much money, they won't be able to earn enough income to pay it back. So, the short answer is this: Yes, a bond market can theoretically grow indefinitely but, no, it won't happen in the real world.
Here's the long answer:
Whether a company can pay back its debt depends on how it uses the money. When a company issues bonds, it is a way of raising capital through debt. For investors, a bond is an investment, but for an issuing company, it's debt; the company is borrowing money from investors and promising to pay it back through a special type of contract called a bond. The money raised by issuing bonds will be used to expand company operations. Increasing production capacity in this manner increases costs, so a company will only increase operations to the point that MC = MR. In other words, as costs increase, the company will stop increasing production once the cost of 1 additional unit of output will exceed the revenues generated thereby creating a net marginal loss.
If a company issues bonds for an amount of debt that will expand operations beyond the point of profit maximization (MC = MR), then the cost of that debt will begin to exceed the revenues generated by borrowing the money at all, leading to a negative return on investment for the company. The cost of repaying the money will be more than they earn.
Under market efficiency, the total value of the bond market will be worth the amount that company's will issue for a sum total of all debt issued in maximizing profit. This assumes, of course, that no company issues equity, which frequently has lower cost of capital. This also assumes an efficient market, which simply isn't true. These assumptions allow us to illustrate theoretical examples such as the upper limits of bond market value, though.