The US won't charge you anything for taking a bass out of their country (unless it takes your suitcase over-weight and into excess baggage).
UK Customs will charge you Import Duty on the cost of the bass, and then VAT on the cost of the bass PLUS the Import Duty.
That said, I brought a bass through Heathrow earlier this year, declared it on arrival, and they were quite helpful on the assessment, especially since the UK£/US$ rate had moved sharply against me over the period.