Paul Ryan also had a social security plan which he published the same year as Bush and the White House purposefully rejected.

He would allow up to 1/2 your contribution of Social Security Taxes (both your personal contributions as well as your employer's contributions) to be diverted to a private account.

Bush on the other hand would allow up to 1/3 of your contributions to a max of $1000 a year (plan 2) or 1/6th of your contributions with no cap (plan 1).

The Bush White House specifically rejected the Paul Ryan plan for it would add $2.4 Trillion dollars to the deficit over 10 years. The reason why it would add about 2 trillion dollars was that you still had to fund all the current social security users (old people and disabled) while still allowing 1/2 of the contributions be diverted to private accounts.

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The first three Bush plans really didn't improve Social Security's financial shape, they used the excuse of the minor financial problems that social security would have decades later as an excuse to change the program fundamentally by privatizing it.

The fourth plan Bush suggested (mean testing the program) would have helped Social Security financial state. Of course another way of mean testing it was (that the Democrats were suggesting) by removing the cap on social security contributions. The Republicans solution was less benefits, the Democrat solution was more Revenues from the rich so that they would not have a ceiling on contributions.