Though we are in the political and geographic heart of Europe - where the East meets north and south as well as its old adversary the West - this is no clandestine code. Mr Randall is marking the kilometres shown on the car's clock, and noting that the journey starts at 1.27pm precisely.
For tour operators, even specialist cultural companies like Mr Randall's, precision is everything. So an inspection visit like this is equally concerned with how long a coach excursion would take as it is with the authenticity of the rococo frescos in the recital room.
Out target is Dolna Krupa, a handsome old palace 70.1km (precisely) north of the Slovak capital. This is where Beethoven composed what is fondly referred to on the CD label here as the "Moonshine Sonata".
This year, Martin Randall Travel will organise 130 cultural tours for small groups, mainly in Europe. Mr Randall's main objective was to decide whether Slovakia merits more than just a port of call on the Austro-Hungarian Music Festival cruise down the Danube. By the time the hour-long, hair- raising drive squeals to an end, the omens are not looking good.
"If one drove at a sensible place it would take at least an hour and a quarter to get here from Bratislava. For an afternoon excursion, that's a long drive, and it's not a particularly attractive journey either," he says.
Beside the baroque palace is a small annexe. The cottage where Beethoven is said to have written his Opus 27 in 1802 has been dedicated as a museum to the composer. This being rural Slovakia, where Soviet influences still prevail, we can't go in even though it is only 2.30pm (exactly). So Mr Randall peers through the grubby glass at the handsome harpsichord.
More luck at the palace itself, where Mr Randall's arrival as a possible customer gets the door unlocked. The attraction of a chamber recital in the home of Beethoven's patron could be considerable, and the room is ideal for a small group. The fresco, featuring a cheerfully ascending Apollo, wins the inspector's approval: "I'd date it from 1760, and say it was recased in 1830."
Mr Randall works with his hands, clapping them to test the room's reverberation time and trilling them across the keyboard of the shiny new grand piano in the centre. Less impressive is the lighting, a communist-era sphere of stainless steel that looks as if a Sputnik has crashed through the ceiling. Then the tour operator, mindful of his responsibility for every aspect of his client's holiday, prods at some uncomfortable-looking chairs. "Beethoven would have been surprised," he mutters diplomatically.
Beyond some dreadful brown curtains lies an expansive lawn, draped with willows. Under communism, composers came here for inspiration. How inspired they felt being downwind from a brewery, or performing in the concrete arena that blots the landscape, is debatable.
Clients would be unlikely to approve. Since 1982, Martin Randall has designed and operated unashamedly up-market, highbrow holidays. Each tour is accompanied by an art historian, archaeologist or musicologist. An eight-day tour of Prague and South Bohemia, comparable to the potential Slovakian safari, costs pounds 1,240. For that sort of price, people expect more than a touch of class. They expect every detail to be right.
For the journey back to Bratislava, we take the "wine route" through a much more pleasing, sub-Burgundian landscape. Mr Randall remains unconvinced about Slovakia, though the appearance of a castle or two on the horizon improves his humour.
Back in the capital, the prospects get a further boost when he finds in an antique shop an ideal engraving for next year's brochure. No lurid colour prints for Martin Randall Travel - the brochure is black and white, relying on the power of assiduously chosen engravings. But the style conceals the pace-setting nature of the company. "I can guarantee that if Slovakia appears in our brochure in 1998, it will appear in at least two other brochures in 1999, and at least 10 by 2001," Mr Randall says.
To get the country on the track to tourism success, Martin Randall has to do more than verify the cultural credentials. He must negotiate with airlines and coach companies to get clients to a place with no direct flights from Britain, and find friendly, comfortable hotels in a country where such a phrase is an oxymoron. That kind of thought, coupled with the imaginative motoring style of the hosts, could drive you to moonshine.
Martin Randall Travel is based at 10 Barley Mow Passage, London W4 4PH (0181-742 3355, fax 0181-742 1066)