Bike pump for compression testing?

He was probably talking about doing a leak down test rather than a compression test.
I have a test kit that connects to the airline and basically blows air into a cylinder that is in a position with both valves closed, obviously if air blows out of exhaust the the exhaust valve is leaking, if it blows up the inlet the inlet valve is leaking, if it blows up through dip stick tube then it is blowing past the rings. Also in a few cases kit blows into the cooling system and confirms gasket failure or cracked head. A gauge measures the percentage of the leak.

A compression check might show a problem but it doesn't show you where that problem is.
My leak down machine is regulated to around 50 psi, you could easily pump bike tyres up to 50 with a hand pump. Admittedly higher test pressures nearer to compression pressures would show a fault quicker but it is very difficult to hold the engine stationary at those pressures.
I've found lots of faults using the lower pressure my machine uses. Once found a crack in a bore around half way down due to coolant level rising as soon as piston was lower than the crack. At 50 psi it is still difficult to hold the engine stationary using a socket on the crank pulley.

And what do you mean "back in the day" why don't you still use leak down for diagnostics?