Bus from LHR to Cambridge

Yes, direct buses depart about hourly; see www.nationalexpress.com.

I just tried the National Express "find your journey" out of curiosity. The bus stop for Cambridge city centre is called Parkside.

It looks like there are no buses in the wee hours of the morning. The OP indicates arrival time 3:00 (that's 3 o'clock in the morning, yes?) so they would have to wait until around 7 a.m. for the earliest bus, according to what I found. If the OP meant 3:00 p.m. (i.e., 15:00 military time) then no problem, buses do seem to run about every hour.

There are almost no 3:00 arrivals at Heathrow, since there are very strict rules for night flights at the airport (it is more or less closed between 22:30 and 06:00 if I'm not mistaken). So I presume the OP means they arrive around 15:00.

There is typically one coach an hour from Heathrow to Cambridge but they aren't the same time each hour because half go via Luton and the other half via Stansted. You haven't indicated what terminal you are arriving in for the appropriate time.

The 24 hour clock issue would have been more important in the other direction as there are coaches leaving Cambridge for Heathrow at 02:05, 03:05 etc.

Thanks for the information on the LHR bus to Cambridge. Yes, we will be arriving at LHR at 15:00, so I reckon we'll find a bus ca. that time.

We just did this last week. Easy peasy! We waited to buy tickets at the central bus station at LHR, as a forum member said he had a hard time changing the time of his ticket (bought online) when he landed early. In fact our plane landed over an hour early also. I got tickets for the 10:55 coach (which takes 2h20). Then I realized that the 10:05 coach was boarding right then (I hadn't looked at trip times earlier than 10:55, as I hadn't expected to arrive early), so I went out and asked the coach driver if I could use that ticket and he nicely said sure (!) but that he'd arrive in Cambridge at about the same time as the 10:55.

Those routed via Luton take about half an hour longer than those via Stansted, on the schedule at least. The latter ones carry on to Norwich.

Thanks, all, again. We will try for the bus that reaches Cambridge via Stansted.

Yes, the National Express Coach goes from LHR to Cambridge. We took the coach last august.
Here's the link to my trip to Cambridge and my experiences with riding the Coach to Cambridge

https://community.ricksteves.com/travel-forum/trip-reports/summer-study-programme-and-cambridge-uk-trip-report

Note, the price difference between last minute walk up tickets and the non-refundable, purchase in advance tickets
and
sometimes the bus is labeled "Norwich" but stops at Cambridge.
The bus I took stopped at Stansted airport, so if you flew into that airport, you would save about an hour of coach travel time.

The coach stops on the sidewalk at Parker's piece, which is a park. From here, you could walk to your hotel or take an uber or taxi.