Will I get a bill or statement each time I submit a meter reading. Such that I can monitor the tariffs being applied

When you receive your reminder email from Bulb send in your readings within 2 days, that way they will use actual readings, then they will calculate your usage for that month and send an email statement usually within a couple of days.
All the necessary info will be on the statement (PDF) which can be downloaded.

You get a statement once a month NOT every time you submit readings.

I joined in September 2018 and have just got my first statement - they are now flooding in one by one (30 April 2019)