GDPR concerns itself with the processing, storage, and transmission of personal data. Sending a single email to a single person counts as processing data. To process the personal data you have to have a lawful basis to have/process that data. There are rules about processing the data of data subjects (GDPR) and there are rules about communication/marketing to data subjects (Privacy and Electronic Communication Regulations).
As for consent, don't send a second email. That's asking for trouble. Honda, Flybe, and others were fined (under PECR) for doing just that. Don't think of it as 'how long do you wait until you can conclude they have not given consent', think of it as 'I haven't received an indication of their consent through a positive, affirmative action, so I can only treat them as not having given consent'.
If they do give consent, record it. You cannot infer nor assume you have consent through inaction, no response, etc.
Currently, there is a "soft opt-in" that allows you to market electronically (and a newsletter counts as marketing) to existing customers if 1) the product you are marketing is allied or similar to the product or service they already receive(d) from you, 2) there is an opt-out option in every communication, 3) they were told at the time you gathered their personal data that you wish to market to them and they had a chance to opt-out at that point, 4) and the email you use to communicate with them was the one gathered at that time.
Giving a business card out does not give consent to process the data. It cannot count as 'consent' unless there is a verifiable, recorded positive affirmative action recording the consent, when it was gained, and what - exactly - they were consenting to. Using the data on the card is more likely to be covered under the legitimate interest lawful basis.