If the 1099-B shows, truly, $100 of gross proceeds, you probably don't need to worry about this very much.
Your easiest course of action is to say you have zero basis. You'll probably pay a federal rate of 15%, so $15 on the $100. (BTW, we do this when someone has small transactions for which basis isn't available and the cost of coming up with a good number for those transactions isn't economical.)
Note: You might also be subject to the 0% long-term capital gains rate if you're in the 10% or 15% tax bracket which mean you really don't need to worry about this. If you want to learn more about how the zero percent capital gains rate works, this blog post explains the math:http://evergreensmallbusiness.com/income-tax-buckets-not-income-tax-brackets/
If it makes you feel better, you can consider the $15 of tax or whatever not the tax... but the money you're paying for avoiding two decades of record-keeping and for avoiding wasting time trying to come up with a better number today.
And a final option: You probably could use an estimate. But I'd be very conservative. E.g., if you thought you paid $40 to $50 way back when, I'd probably use $35 as your basis estimate. Note that, using your example numbers and a 15% rate, this saves you $5 of the $15 of tax. So not much.
Final comment: If the number is $10,000 or $100,000, I would do the accounting to come up with a good number.