Drug-related convictions automatically bar anyone from entering the USA, on the grounds of 'moral turpitude'. Any visa application will, in the first instance, be refused but then passed on to Washington as an application for a 'waiver of permanent ineligibility'. If such a waiver is granted, the visa application will then be reconsidered. The process is extremely lengthy. It would certainly be unwise to apply now for travel before the end of this year. (The longest wait I've seen reported, here on AB was 10 months. The applicant was then refused a visa because of two convictions of driving without insurance).
There have been plenty of people who've reported that they've entered the USA (illegally) by simply 'forgetting' about their convictions and using the Visa Waiver Program. However, since the introduction of the ESTA system, US immigration officials now have a longer time to process applications and to run checks upon applicants. While the UK is not allowed (under EU privacy laws) to make British criminal records freely available to overseas governments, a great deal of information of information is almost certainly passed on under the guise of 'anti-terrorism'. (The UK is allowed to provide information where the US authorities make a specific request for information. It's quite possible that such requests are now being made in respect of most travellers).
Unless you're prepared to 'risk it', you should apply for a visa at least a year before you intend to travel, and not book anything until you've heard the result of your visa application. (The Rehabilitation of Offenders Act is not recognised by the USA, so offences never become 'spent'. However the fairly long period of time since your conviction might work in your favour).
Chris