If your string is only 1 and 0 you could simply treat it like a number and convert it to another base. Hex or base10. This would shrink your representation of the data, if you have to query the table, just convert your query string prior to running it.
This may also make it easier to handle the data.
You may have to split your data up into several strings, depending on the limitations of the conversion program. so as and example 00111011101010000110 => 0011101+1101010+000110 => 48863+545345+879