As far as I know, there's no way to search for a specific transit without searching for it by date. However, with Venus transits, it's pretty easy to narrow down the date. Venus is always within 48 degrees of the sun, usually closer, and it takes a year, give or take up to a month or so, to transit the whole zodiac. That means Venus will always trine your ascendant twice a year, and it happens at the times of year when the sun is within one or two signs of where Venus has to be to trine your ascendant. Venus conjuncts your ascendant once a year, when the sun is within a sign or two of your ascendant.
For example, I have my ascendant at 3 degrees Capricorn. That means I get Venus trines to my ascendant when Venus has just entered Taurus and when it's just entered Virgo. So, if I were looking for my next Venus trine ascendant date, I would limit my search to the springtime/early summer or the late summer/early autumn, whichever is coming up soonest. I would also start by checking for Venus's current position, and also check to see if it goes retrograde anytime soon, because a retrograde changes how fast it moves. If I did all that today, I would know that the next Venus trine to my ascendant will happen in the middle of May (I actually already knew that because I heard a podcast about the upcoming transits, but if I didn't, that's how I'd find out). For Venus conjunct my ascendant, I know to look for winter or late fall dates, because that's when Venus can be in early Capricorn, with the most likely dates being in December and January.
Venus doesn't move more than one degree in a day. So, if you find a date when Venus is within a degree of trine or conjunction to your ascendant, that's going to be it.