I use either of these two Bestek inverters. Both work. Both cost about £40 on Amazon. A 2-amp 42-volt e-bike charger consumes roughly 80-watts of mains power.
The first is rated at a constant 400w (about 1000w peak) when connected direct to a vehicle battery, or 150w when connected via an accessory or cigarette socket (due to the limits of in-vehicle wiring/fusing and the current being consumed). It's the more common type of inverter, the lower cost "modified sine wave", aka "square wave". It's not a pure emulation of mains electricity, but works fine with an SMPS e-bike charger. This one gets good reviews, and I haven't had any issues at all with it.
This second one is rated at 300w (about 700w peak). In theory, whilst a little lower powered it is the better/kinder inverter being "pure" sine wave as household electricity is. Some "fussy" reviewers do suggest it isn't as perfect a sine wave as "proper mains", and generates some interference with some devices. Again limited to 150w through a cigarette lighter socket, you'd need extra cost cables (£12) if you wanted to connect this inverter direct to a battery to get the full 300w available (to power a DVD/TV etc).
Both inverters also feature 1A and 2.4A USB charging sockets. Both inverters use cooling fans (which do generate noise). Both inverters (as with all makes of inverter) can kick the crap out of your car/leisure battery in double quick time, and are designed to be used with the engine/alternator running. Both inverters feature low-voltage/overheat/over-voltage shut-off, and are fused for safety.
Neither inverter is going to generate "perfect" electricity at this sort of price, but frankly, an e-bike charger really isn't that fussy.