After bowling the Baggy Greens out early on day three, the Three Lions found themselves on 49-3 before Bell hit 105 not out and Pietersen racked up a solid 44 to leave the hosts with a lead of 202 at stumps on 234-5.
Botham has praised the pair for salvaging England's hopes of victory and believes that Bell and Tim Bresnan can put the hosts in a commanding position on Monday when they return to the crease.
"Kevin Pietersen's partnership with Bell was crucial," Botham told Sky Sports News. "That steadied the ship when we were all over the place. The Aussies were bouncing around with [Joe] Root, [Alastair] Cook and [Jonathan] Trott out and England had to stop the rot.
"KP played well and I think [Jonathan] Bairstow also played better today; he was much more confident and playing his shots - and I'd much rather see him playing like that than he did in the first innings.
"In terms of tomorrow, they are saying there will be some weather around in the afternoon but England are in the ascendancy and they don't have to worry about that - they'll just go out and bat as long as they can. If they get to 300 I think they'll feel pretty good and if they get above that they'll be very happy, considering where they were at one stage."
The ton was Bell's third of the Ashes.