TL;DR: It's a common twist on a different common idiom; in this form, it means "What you just said is clearly false."
As sure/true as I'm [fill in the blank of what I'm doing or am] is a common idiom used to mean that something is definitely true.
The blank can be filled in lots of different ways; [as sure] as I'm alive is the earliest form I can find, for example in this ostensibly 17th century work (snippet view), this "Epilogue" from 1756, and this English-Swedish dictionary from 1757.
The most common formulation today might be the (usually American English) [as] sure as I'm standing here (M-W) but it is often shifted for comical effect. For example:
A lot of times, I'll start a sentence with the phrase, "As sure as I'm fat and bald, . . ." (Jud Heathcote & Jack Ebling, Jud: A Magical Journey, 1995)
So long as whatever fills in the blank is obviously true, the original meaning of the idiom remains.
However, if the end of the phrase is patently untrue then the meaning of the idiom is flipped to mean the rest of what I'm talking about is also false.
Some of these "flipped" versions have passed into semi-idiomatic use, such as sure as I'm a foot high (apparently Irish slang) and Inspector Japp's statement, used when one is obviously not riding a bicycle.
While a bicycle or bike is the most common thing (not) being ridden, there are other variants of the form true/sure as I'm riding this [thing I am obviously not riding], such as:
I know, I believe you. As sure as I'm riding this unicycle. ;) (discussion comment, "Re: Outlander...not to be missed IMHO", Calis Beach Forum, 2015)
I’ll tell you of the Queens of the Highway
And believe me I’ll tell you no flannel
It was told me first hand by the lads on the trucks
It’s as true as I’m riding this camel
(Bernard Wrigley & Henry Boot, Queens of the Highway lyrics) (camel might be the second most common thing not being ridden)
Ancient civilianisation discovered this. No it’s true, come on, would I lie to you? As sure as I’m riding this Unicorn, Octopus therapy works. Next time one of your friends feels a little down, a bit saggy at the edges, try slapping them in the face with a 30 pound Enteroctopus dofleini, and I bet you things will start to improve from that point onwards (british-and-bonkers, "Octopus Love", via Tumblr)
Most of the above appear to be UK sources, but sure as I'm riding this bike has also apparently made it at least to New Zealand.