“As true as I’m riding this bicycle”

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.

It appears to be an actual saying. From Irish Sayings with Interpretation:

"As true as I'm riding this bike"

This is said when you're not riding a bike, but emphasises your sincerity!

Or more likely, the complete lack of sincerity.

It would appear to be delivered in an ironic manner, and in this following case it seems to be sincere:

What's that I hear you say? By 1947 no-one was shooting anyone, least of all Geordie holidaymakers on the A66? And your Official History of Tottenham Hotspur gives no mention of a William Butcher, or for that matter of his hat? (strange that, neither does mine). Well, it's all true--as true as I'm riding this bike. And if you'll believe it, well, you'll probably believe about The Songbook as well.

...but then later, the author implies that all is tongue-in-cheek.

we'll remind them of Great Uncle Paddy Flanahan O'Butcher, the famous minstrel of County Cork, and inventor of the boiled potato,

In the transcript from the dramatization of The Western Star, it is quite obvious that Japp does not believe the person he is interrogating when he uses the phrase...

   Japp: Here we are again. Sinister chinaman, little yellow gods, threatening letters.
Suspect: No, it's all true.
   Japp: Oh, yes. It's as true as I'm riding this bicycle.  

'As true as i'm riding this bicycle' often found as 'as true as I'm riding this bike' is a jocular phrase used to indicate that the speaker does not believe a putative fact which has been stated by another, or that their own previous statement is not reliable.

Examples of use

Bang Bang Beirut
By Ray Cooney, Tony Hilton

Fred: She's my agent and personal manager.
Farina: get lost.
Fred: It's true.
Farina: yes, about as true as I'm riding this bicycle. And what about that little boy up there, who's he?
Fred: That's not a little boy, that's Jimmy Clitheroe.
Farina: i didn't come up yesterday, you know.

Innocent on the Run
By Deric Barry

Charlie... told Ricky he'd met some beautiful American girls, who were mad for him, but he had to tell them all that he had to get back to his ship, as he was the captain, and noone would know what to do if he wasn't there supervising.
Doc overheard him, and he stiuck his head through the serving hatch. 'Get lost, you grease monkey.' he shouted. 'The only girls you met were in your dreams.'
Charlie laughed. 'It's true Doc, honest. As true as I'm riding this bike.'
'Get back down below, you've been having those funny hallucinations again.'