You can flush the engine clean wth engine oil
Use something a little cheaper, but still decent, like halfords motorcycle oil. Fill up as per normal, got for a ride (maybe 10 miles or 30 mins) then when you get back, drain the halfords oil, refill with something proper good (maybe change the oil filter too actually) like castrol or motul.
Oil that looks dirty shows that its doing its job, its suspending dirt and keeping it from clogging up oil galleys etc etc. So long as there arn't metal shards or whatever in the oil, then thats pretty much ok