USA and UK government report on plane emissions: 200% difference... which is right?
I've looked into this briefly and noticed a few things that are worth pointing out.  First, your EPA table looks like it was based on Table 8 of this EPA pdf:

https://www.epa.gov/sites/production/files/2018-03/documents/emission-factors_mar_2018_0.pdf

There’s a note in the table that,


  Air Travel factors from 2017 Guidelines to Defra / DECC's GHG
  Conversion Factors for Company Reporting. Version 1.0 August 2017.


So, with a lovely bit of irony, those EPA air travel numbers are taken from the UK/DECC/Defra, which are available here:

https://www.gov.uk/government/publications/greenhouse-gas-reporting-conversion-factors-2017

Note that they’ve translated the names of the air travel distance categories so they make sense in the US market:


US short-haul (&lt; 300 mi) = UK domestic (UK to UK)
US medium-haul (300 - 2300 mi) = UK short-haul (&lt; 3700 km)
US long-haul (> 2300 mi) = UK long-haul (> 3700 km)


Taking some numbers from US short-haul/UK domestic as an example, the CO2 emissions are,

0.14002 kgCO2e/pass km = 140.02 gCO2e/pass km = 225.3 gCO2e/pass mi

which is just basic units conversion and agrees with your EPA table and the EPA pdf.  The same is true for the CO2 emissions in the other distance categories.  Note that the EPA are using the numbers for the CO2e emissions without radiative forcing feedbacks from water vapor, contrails, NOx, etc., which is the dark blue portion of the bars in your plot from the BBC.  You should be comparing that portion of the emissions, not the full bar including the light blue.

There's a further problem with the CH4 and N2O values in your EPA table.  Taking the same example as above but for CH4 emissions,

0.00006 kgCO2e/pass km = 0.06 gCO2e/pass km = 0.097 gCO2e/pass mi = 0.0039 gCH4/pass mi

This is correct in the EPA pdf, but has been mis-transcribed in your EPA table as 3.9 gCH4/pass mi.  Oops! someone got confused between grams and kilograms, and they've made the same mistake in the CH4 and N2O entries for all modes of transport.  They’ve then used this to calculate the overall GWP column, so their values are oversensitive to CH4 and N2O:

GWP = 225*1 + 3.9*25 + 7.2*298 = 2468.1

The correct calculation is,

GWP = 225*1 + 3.9e-3*25 + 7.2e-3*298 = 227

The bottom line is that I think the GWP column in your EPA table is nonsense and the aircraft emissions factors have the same source (albeit the BBC are probably using more recent UK emission factors).  The respective CO2 emissions for cars in the sources I've linked to aren't wildly different (297 gCO2/mi in UK, 343 gCO2/mi in US) and for motorcycles are almost identical (183 gCO2/mi in UK, 189 gCO2/mi in US).