I don't think it's quite true to say that after 20 years we would be left with nothing. If it encourages more people to take the bus instead of driving then it would decrease traffic and pollution. Although in cases where buses are already in demand, adding new routes or increasing bus frequency on existing routes would be a better use of money.
It's actually worse than that, because you've essentially taken out an unsecured loan of £100bn and spent it on something which neither increases ongoing tax revenue or asset value, so you now have to cut other spending to pay it off. Which is why governments and businesses separate capital expenditure (building things) from current expenditure (doing things) very carefully.
The lingering impact of millions of people realising that bus travel is actually a good idea and that cars aren't necessary in a lot of cases. How terrible!
It's for this reason that saying 'we could spend the money on making buses free for a N years' is meaningless. It would be more sensible to say 'we should spend the £Nbn we spend on maintaining the motorway network on free buses' because those types of spending are equivalent.