[iMore Question]

20 seconds isn't enough time to dig my phone out of my purse and answer it.

[SwitchBeach]

Contact your service provider.

[IAmSixNine]

Clean out your purse? LOL maybe attach the phone via a clip to the purse straps for easier access.
SwitchBeach has the correct answer, thats usually on the carrier side.

[tai4de2]

It is possible to control more details about call forwarding than the iPhone's menus offer, via GSM supplementary service codes.

You didn't mention which carrier you are on, but look at the "Call forwarding" article on Wikipedia (I can't post links yet, sorry). There's a table in the "Mobile (cell) phones" section, and an explanation that includes specifying the delay time before forwarding occurs.

[anon(9602380)]

20 seconds isn't enough time to dig my phone out of my purse and answer it.

Welcome to iMore. One thing you could do is create your own ringtone. This will allow you to set it to a length that is more suitable for your needs. This link will give you the instructions on how to make custom ringtones using iTunes. Thanks goes to Highrisedrifter for the guide on how to do it. You can also create ringtones in the Garageband app if you own a Mac. Very simple to do either way. Garageband allows a little more flexibility with what you can do to the custom ringtone.